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Basic Statistics Concepts Marketing Logistics

Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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Page 1: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Basic Statistics Concepts

Marketing Logistics

Page 2: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Basic Statistics Concepts

Including: histograms, means, normal distributions,

standard deviations.

Page 3: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Basic Statistics Concepts

Developing a histogram.

Page 4: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Developing a Histogram

• Let’s say we are looking at the test scores of 42 students.

• For the sake of our discussion, we will call each test score an “observation.”

• Therefore, we have 42 observations.

• The next slide shows the 42 test scores or observations.

Page 5: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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Observations

Page 6: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Plotting Scores on a Histogram

• We decide to start figuring out how many times students made a specific score.

• In other words, how many students got a score of 85? How many got a 95? And so on…

• We list all the scores, then begin recording how many times a student got that score.

• The next slide shows a list of all the scores.

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Page 8: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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Scores made by students

Page 9: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Back to Our Observations.

Page 10: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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Observations

Page 11: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Back to Our Observations.

• How many times did someone get a 70?

• Look on the next slide and count the number of scores of 70.

Page 12: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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Observations

Page 13: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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There are six

scores of 70Observations

Page 14: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Back to Our List of Scores

Page 15: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

55 60 65 70 75 80 85 90 95

Back to Our List of Scores

Page 16: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1

Back to Our List of Scores

For each of thescores of 70 wemake one mark.

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

We continue to count the number of specific observations having a specific score.

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

We continue to count the number of specific observations having a specific score.

We are making

what is called a

“histogram.”

Page 19: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

HistogramMany times our histogram will end up looking much like this:

Page 20: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

HistogramThis is what is called a “normal distribution.”

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

This is what is called a “normal distribution.”

When things occur at what we would call random, they frequently fall into a normal distribution.

Histogram

Page 22: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

This is what is called a “normal distribution.”

In a normal distribution the highest number of observations occurs at the mean.

Histogram

Page 23: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

This is what is called a “normal distribution.”

In a normal distribution the highest number of observations occurs at the mean. There were seven scores of 75.

Histogram

Page 24: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

This is what is called a “normal distribution.”

Then they tend to taper off as you go to the higher scores…

Histogram

Page 25: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

This is what is called a “normal distribution.”

Then they tend to taper off as you go to the higher scores. Only six scores of 80…

Histogram

Page 26: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

This is what is called a “normal distribution.”

Then they tend to taper off as you go to the higher scores. Only four scores of 85…

Histogram

Page 27: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

This is what is called a “normal distribution.”

Then they tend to taper off as you go to the higher scores. Three scores of 90.

Histogram

Page 28: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

This is what is called a “normal distribution.”

Then they tend to taper off as you go to the higher scores. Two scores of 95.

Histogram

Page 29: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

This is what is called a “normal distribution.”

Below the mean, scores tend to taper off, usually at about an identical rate as the scores we just looked at that were above the mean.

Histogram

Page 30: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

This is what is called a “normal distribution.”

This phenomenon often occurs in events that we consider to be at random…

Histogram

Page 31: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

This is what is called a “normal distribution.”

…the scores tend to be distributed in a predictable way…

Histogram

Page 32: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

This is what is called a “normal distribution.”

…so we say it’s a…Histogram

Page 33: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

This is what is called a “normal distribution.”

…so we say it’s a…Histogram

Page 34: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

This is what is called a “normal distribution.”

HistogramIt is usually graphed somewhat like this:

Page 35: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

HistogramIt is usually graphed somewhat like this:

This is what is called a “normal distribution.”

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

HistogramIt is usually graphed somewhat like this:

While this is a rather crude graphing, the next slide shows several examples of normal distributions.

Page 37: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Total Order Cycle with Variability

2. Order entry and processing

Frequency:

1 2 3

1. Order preparation and transmittal

Frequency:

1 2 3

3. Order picking or production

Frequency:

1 9

Frequency:

TOTAL

3.5 days 8 20 days

5. Transportation

Frequency:

1 3 5

6. Customer receiving

Frequency:

.5 1 1.5

From instructional material from “Strategic Logistics Management” by Stock and Lambert (2001).

Page 38: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Total Order Cycle with Variability

2. Order entry and processing

Frequency:

1 2 3

1. Order preparation and transmittal

Frequency:

1 2 3

3. Order picking or production

Frequency:

1 9

Frequency:

TOTAL

3.5 days 8 20 days

5. Transportation

Frequency:

1 3 5

6. Customer receiving

Frequency:

.5 1 1.5

The line in the middle of each normal distribution indicates the average or, more correctly, the “mean.” It’s the place where we have the highest number of observations.

From instructional material from “Strategic Logistics Management” by Stock and Lambert (2001).

Page 39: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Total Order Cycle with Variability

2. Order entry and processing

Frequency:

1 2 3

1. Order preparation and transmittal

Frequency:

1 2 3

3. Order picking or production

Frequency:

1 9

Frequency:

TOTAL

3.5 days 8 20 days

5. Transportation

Frequency:

1 3 5

6. Customer receiving

Frequency:

.5 1 1.5

Mean or average of about 2.Mean of just under 1

Mean of about 10.

Mean of 1

Mean of about 3

The line in the middle of each normal distribution indicates the average or, more correctly, the “mean.” It’s the place where we have the highest number of observations.

From instructional material from “Strategic Logistics Management” by Stock and Lambert (2001).

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

HistogramIf the highest part of our histrogram is on 75, it stands to reason that 75 is our mean of our test scores.

Page 41: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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Observations

Sure enough, if you were to average out all of ourobservations…

Page 42: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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Mean = 75

Observations

Sure enough, if you were to average out all of our observations…

You get a mean of 75.

Page 43: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

A mean can be a good predictor…

• A mean or average can often help me predict what will happen in the future.

• For instance, if students usually get a mean of 75 on tests, by giving basically the same kinds of tests, an instructor can usually predict that in the future students will usually score an average of 75 on the test.

Page 44: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

A mean can be a good predictor, but…

• Sometimes a mean is not enough for a prediction or determination.

Page 45: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

A mean can be a good predictor, but…

• Sometimes a mean is not enough for a prediction or determination.

• For instance, if I tell you that the average, or mean, depth of the Mississippi River is about 18 feet, I’m not giving you a clear picture of the nature of the river.

Page 46: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

A mean can be a good predictor, but…

• Sometimes a mean is not enough for a prediction or determination.

• For instance, if I tell you that the average, or mean, depth of the Mississippi River is about 18 feet, I’m not giving you a clear picture of the nature of the river.

• That’s because at its headwaters, the river averages around 3 feet deep. But in certain places around New Orleans, it is 200 feet deep.

Page 47: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Mississippi River Surface

Mississippi River Bottom

3 feet

200 feet

Headwaters New Orleans

Mean depth = 18 feet

Page 48: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Mississippi River Surface

Mississippi River Bottom

3 feet

200 feet

Mean depth = 18 feet

There is a big difference between 3 feet and 200 feet.

Headwaters New Orleans

Page 49: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Mississippi River Surface

Mississippi River Bottom

3 feet

200 feet

Mean depth = 18 feet

There is a big difference between 3 feet and 200 feet.

Headwaters New Orleans

That means my description of the Mississippi River as having an 18-foot mean depth really doesn’t tell me much.

Page 50: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Mississippi River Surface

Mississippi River Bottom

3 feet

200 feet

Mean depth = 18 feet

There is a big difference between 3 feet and 200 feet.

Headwaters New Orleans

To get an accurate picture or prediction of Mississippi River depth, I need to find

out how much variation there is around the mean. In other words, at different places

along the river, how much different is the depth at that place, compared to the mean?

That means my description of the Mississippi River as having an 18-foot mean depth really doesn’t tell me much.

Page 51: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Mississippi River Surface

Mississippi River Bottom

3 feet

200 feet

Mean depth = 18 feet

Headwaters New Orleans

To get an accurate picture or prediction of Mississippi River depth, I need to find

out how much variation there is around the mean. In other words, at different places

along the river, how much different is the depth at that place, compared to the mean.

Depth 5 feet, 13 feet less than mean of 18 feet

Page 52: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Mississippi River Surface

Mississippi River Bottom

3 feet

200 feet

Mean depth = 18 feet

Headwaters New Orleans

To get an accurate picture or prediction of Mississippi River depth, I need to find

out how much variation there is around the mean. In other words, at different places

along the river, how much different is the depth at that place, compared to the mean.

Depth 100 feet, 82 feet more than mean of 18 feet

Page 53: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Mississippi River Surface

Mississippi River Bottom

3 feet

200 feet

Mean depth = 18 feet

Headwaters New Orleans

To get an accurate picture or prediction of Mississippi River depth, I need to find

out how much variation there is around the mean. In other words, at different places

along the river, how much different is the depth at that place, compared to the mean.

Depth 190 feet, 172 feet more than mean of 18 feet

Page 54: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Mississippi River Surface

Mississippi River Bottom

3 feet

200 feet

Mean depth = 18 feet

Headwaters New Orleans

To get an accurate picture or prediction of Mississippi River depth, I need to find

out how much variation there is around the mean. In other words, at different places

along the river, how much different is the depth at that place, compared to the mean.

And so on…

Page 55: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Mississippi River Surface

Mississippi River Bottom

3 feet

200 feet

Mean depth = 18 feet

Headwaters New Orleans

To get an accurate picture or prediction of Mississippi River depth, I need to find

out how much variation there is around the mean. In other words, at different places

along the river, how much different is the depth at that place, compared to the mean.

If I can now average all of these measurements-- how far away each depth is from the mean of18 feet – I can get a clearer picture of how deepthe Mississippi River actually is.

Page 56: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Mississippi River Surface

Mississippi River Bottom

3 feet

200 feet

Mean depth = 18 feet

Headwaters New Orleans

To get an accurate picture or prediction of Mississippi River depth, I need to find

out how much variation there is around the mean. In other words, at different places

along the river, how much different is the depth at that place, compared to the mean.

In other words, what I want to know is the“standard deviation” – what is the averageall of the depth measurements are away from the mean of 18 feet.

Page 57: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

In other words, what I want to know is the“standard deviation” – what is the averageall of the depth measurements are away from the mean of 18 feet.

Let’s go back to our test scores.

Page 58: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

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Mean = 75

Observations

Page 59: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• How far away from the mean do the observations generally fall?

Page 60: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• How far away from the mean do the observations generally fall?

• There is a formula to show us…

Page 61: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• How far away from the mean do the observations generally fall?

SD =(Observation – mean)2

N-1

Page 62: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• How far away from the mean do the observations generally fall?

SD =(Observation – mean)2

N-1

To find standard deviation…

Page 63: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• How far away from the mean do the observations generally fall?

• We take the square root of…

SD =(Observation – mean)2

N-1

Page 64: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• How far away from the mean do the observations generally fall?

SD =(Observation – mean)2

N-1

The sum of…

Page 65: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• How far away from the mean do the observations generally fall?

SD =(Observation – mean)2

N-1

The difference between the

observation minus the mean…

Page 66: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• How far away from the mean do the observations generally fall?

SD =(Observation – mean)2

N-1

The difference between the

observation minus the mean…

…Squared…

Page 67: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• How far away from the mean do the observations generally fall?

SD =(Observation – mean)2

N-1

…divided by one less than the number of observations

Page 68: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• Note for the Statistics Police, but something you don’t have to worry about…

SD =(Observation – mean)2

N-1

…divided by one less than the number of observations

N-1 may not always be technically correct. In some cases it should be just N, the number of observations.However, in this classwe will always use N-1.*

*For population use N; for sample use N-1.

Page 69: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• Let’s find the standard deviation for our test score observations…

SD =(Observation – mean)2

N-1

Page 70: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• Let’s begin with just this part of the formula…

SD =(Observation – mean)2

N-1

Page 71: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• Let’s begin with just this part of the formula…

(Observation – mean)2

Page 72: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• Let’s begin with just this part of the formula and look at the test score of 70, one of our observations.

(Observation – mean)2

Page 73: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• Let’s begin with just this part of the formula and look at the test score of 70, one of our observations.

(Observation – mean)2

70

Page 74: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• And let’s include our mean, which we determined to be 75.

(Observation – mean)2

70 75

Page 75: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

(Observation – mean)2

70 75Subtract the mean from the observation, ortake 75 away from 70.

-

Page 76: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

(Observation – mean)2

70 75Subtract the mean from the observation, ortake 75 away from 70.

It equals minus 5.

- = -5

Page 77: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

(Observation – mean)2

70 75- = -5

We cannot have negative numbers, so to

make -5 positive, we square it, since a

negative times a

negative equals

a positive.

Page 78: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

(Observation – mean)2

70 75- = -5 X - 5

= 25

We cannot have negative numbers, so to

make -5 positive, we square it, since a

negative times a

negative equals

a positive.

Page 79: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

(Observation – mean)2

70 75- = -5 X - 5

= 25

We cannot have negative numbers, so to

make -5 positive, we square it, since a

negative times a

negative equals

a positive.This is called a “square.”

Page 80: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

25-57570

Observation Mean

ObservationMinus mean

Observationminus meansquared knownas a“square.”

Expressed another way:

S

Page 81: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

25-57570100-10756525-57570007575

225-157560007575

2557580

Observation Mean Observation minus mean

Observationminus meansquared

We go through all our observations,

subtracting the mean from them and squaring

the results.

Squares

First six observations…

Page 82: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Observation Mean Observation minus mean

Observationminus meansquared

2557580100107585

007575400-2075551001075852557580255758025-57570

Squares

…next seven observations. Rather than have slides showing all the observations…

Page 83: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Observation Mean Observation minus mean

Observationminus meansquared

225157590100107585100-10756525-575702557580

4300

…I will skip to the final four

observations.

Squares

Page 84: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• And come to the next part of our formula…

SD =(Observation – mean)2

N-1

Page 85: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• And come to the next part of our formula…

• …adding up all of the squares.

SD =(Observation – mean)2

N-1

Page 86: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• And come to the next part of our formula…

• …adding up all of the squares.

SD =(Observation – mean)2

Page 87: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

25-57570100-10756525-57570007575

225-157560007575

2557580

Observation Mean Observation minus mean

Observationminus meansquared

Add up all squares

First six observations…

A

D

D

Page 88: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Observation Mean Observation minus mean

Observationminus meansquared

2557580100107585

007575400-2075551001075852557580255758025-57570

Add up all squares

A

D

D

…next seven observations. Rather than have slides showing all the observations…

Page 89: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Observation Mean Observation minus mean

Observationminus meansquared

225157590100107585100-10756525-575702557580

4300

A

D

D

A

D

D

…I will skip to the final four

observations.

Page 90: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Observation Mean Observation minus mean

Observationminus meansquared

225157590100107585100-10756525-575702557580

4300

Sum of squares…total of all

observations.

Page 91: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• We now have some data for our formula…

SD =(Observation – mean)2

N-1

Page 92: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• We now have some data for our formula…

SD =(Observation – mean)2

N-1

Sum of squares

Page 93: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• We now have some data for our formula…

SD = 4300

N-1

Sum of squares

Page 94: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• Now for the next part of our formula…

SD = 4300

N-1

Page 95: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• Now to the next part of our formula…

• …divide the sum of squares by the number of observations minus 1.

SD = N-1

4300

Page 96: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Count the number of observations…

Page 97: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

25-57570100-10756525-57570007575

225-157560007575

2557580

Observation Mean Observation minus mean

Observationminus meansquared

First six

observations…

1

2

3

4

5

6

Count the number of observations…

Page 98: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Observation Mean Observation minus mean

Observationminus meansquared

2557580100107585

007575400-2075551001075852557580255758025-57570

…next seven observations. Rather than have slides showing all the observations…

7

8

9

10

11

12

13

Count the number of observations…

Page 99: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Observation Mean Observation minus mean

Observationminus meansquared

225157590100107585100-10756525-575702557580

4300

Sum of squares

39

40

41

42

Count the number of observations…

…I will skip to the final four

observations.

Page 100: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Observation Mean Observation minus mean

Observationminus meansquared

225157590100107585100-10756525-575702557580

4300

39

40

41

42

Count the number of observations…

There are 42 observations

Sum of squares

Page 101: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

SD = N-1

4300

• More data for the formula…

Page 102: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

SD = N-1

4300

•More data for the formula…

We have 42 observations so n is 42.

Page 103: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

SD = 42-1

4300

•More data for the formula…

We have 42 observations so n is 42.

Page 104: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

SD = 42-1

4300

•More data for the formula…

42 minus 1 is 41.

Page 105: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

SD = 41

4300

•More data for the formula…

42 minus 1 is 41.

Page 106: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

SD = 41

4300

•Process part of the formula…

4300 divided by 41…

Page 107: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

SD = 41

4300

•Process part of the formula…

4300 divided by 41…

= 104.87

…equals

104.87

Page 108: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

SD =

•Finish the formula…

Find the square root of 104.87

104.87

Page 109: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

SD =

•Finish the formula…

Find the square root of 104.87

= 104.87 = 10.24

Which is 10.24

Page 110: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

SD =

•Finish the formula…

Therefore, our standard deviation is 10.24

10.24

Page 111: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

SD =

•This means that our observations average 10.24 away from the mean.

Therefore, our standard deviation is 10.24

10.24

Page 112: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

To Review…

Page 113: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

To Review…

• We developed a histogram…

Page 114: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

55 60 65 70 75 80 85 90 95

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Histogram

Page 115: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

To Review…

• We examined a normal distribution...

Page 116: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

55 60 65 70 75 80 85 90 95

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Normal Distribution

Page 117: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Total Order Cycle with Variability

2. Order entry and processing

Frequency:

1 2 3

1. Order preparation and transmittal

Frequency:

1 2 3

3. Order picking or production

Frequency:

1 9

Frequency:

TOTAL

3.5 days 8 20 days

5. Transportation

Frequency:

1 3 5

6. Customer receiving

Frequency:

.5 1 1.5

Normal Distribution

From instructional material from “Strategic Logistics Management” by Stock and Lambert (2001).

Page 118: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

To Review…

• We learned how to determine standard deviation, or the average of how far observations are different from the mean.

Page 119: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

Standard Deviation

• How far away from the mean do the observations generally fall?

SD =(Observation – mean)2

N-1

Page 120: Basic Statistics Concepts Marketing Logistics. Basic Statistics Concepts Including: histograms, means, normal distributions, standard deviations

End of Program.