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Introductory Statistics Lesson 2.3 A Objective: SSBAT find the mean, median, and mode of data. Standards: M11.E.2.1.1. Measure of Central Tendency A value (number) that represents a typical or central entry of a data set 3 commonly used measures are MEAN, MEDIAN, and MODE. Mean - PowerPoint PPT Presentation
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Introductory Statistics
Lesson 2.3 A
Objective: SSBAT find the mean, median, and mode of data.
Standards: M11.E.2.1.1
Measure of Central Tendency
A value (number) that represents a typical or central entry of a data set
3 commonly used measures are MEAN, MEDIAN, and MODE
Example: The ages of employees in a department are listed. What is the mean age?
34, 27, 50, 45, 41, 37, 24, 57, 40, 38, 62, 44, 39, 40
The mean age of the employees is 41.3 years.
Mean
Add all of the numbers together and Divide by the number of values in the set
Population Mean
represents the population mean
N represents the number of entries in a Population
Sample Mean
represents the sample mean
n represents the number of entries in a Sample
Example: The prices (in dollars) for a sample of roundtrip flights from Chicago, Illinois to Cancun, Mexico are listed. What is the mean price of the flights?
872, 432, 397, 427, 388, 782, 397
= 872 + 432 + 397 + 427 + 388 + 782 + 397
= 3695
=
527.90
The mean price of the flights is about $527.90.
Median
The number that is in the middle of the data when it is ordered from least to greatest
1. Write the numbers in order from least to greatest2. Find the middle number
If there are 2 middle numbers, Add them and divide by 2
Example: Find the Median of the flight prices from 1.
872, 432, 397, 427, 388, 782, 397
388, 397, 397, 427, 432, 782, 872
The Median flight price is $427.
Example: The ages of a sample of fans at a rock concert are listed. Find the median age.
26, 27, 19, 21, 23, 30, 36, 21, 27, 19,
Mode
The number that occurs the most in the data set
If no entry is repeated, there is No Mode
There may be more than 1 mode
Bimodal A data set that has 2 modes
Example: Find the mode of the flight prices from #1.
872, 432, 397, 427, 388, 782, 397
The mode price is $397.
Example: Find the mode of the employee ages.
24, 27, 27, 34, 37, 38, 39, 40, 40, 44, 49, 57
The mode age is 27 and 40
Example: A sample of people were asked which political party they belonged to. The results are in the table below.
What is the Mode of their response?
Political Party Frequency, fDemocrat 34
Republican 56
Other 21
Did not respond 9
The response with the greatest frequency is Republican therefore the MODE is Republican
Example: Find the Mean, Median, and Mode
Football Team Points
Stem Leaf
0 6
1 2 3 3 7
2 0 3 4 4 7 8
3 0 7 8
Key: 1│2 = 12 points
Mean: 22.3
Median: 23.5
Mode: 13 and 24
Example: Find the Mean, Median, and Mode
Entries: 1, 3, 3, 6, 6, 7, 8, 8, 8, 8, 10
Mean: 6.2
Median: 7
Mode: 8
Find the Mean, Median and Mode of the data set.
20, 20, 20, 20, 20, 21, 21, 21, 22, 22, 23, 23, 23, 25, 25, 78
Mean, : 25.3
Median: 21.5
Mode: 20
Which measure of central tendency best describes this data set?
Median
Outlier
A data entry that is a lot bigger or smaller than the other entries in the set
Outliers cause Gaps in the data
Conclusions made from data with outliers can be flawed
MEAN
- There is only one mean for each data set- It is the most commonly- It takes into consideration all data entries- It is affected by Extreme Values – Outliers
MEDIAN
- There is only one median for each data set- Extreme values (outliers) do NOT affect the median
MODE
- Use when you are looking for the most popular item- Use when you have non-numerical data- When no value repeats there is no mode
Homework
Page 75 – 76
#18, 20, 22, 32, 34