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Parameters VS. Statisticsand
Samples & Census
How do we compare statistics and parameters?
M2 Unit 4: Day 3
Statistics VS Parameters
Statistics (for samples) : and
Parameters (for populations) : and
x
S
Today…
You will be given the population parameters and
You will be given a data set for a sample and you will find the statistics and
Then you will compare the statistics to the parameters
x S
Example1For a large population, the mean = 25.1 and the s.d =5.3.
A random sample produced the following data values: 25, 21, 32, 14, 17, 22, 29.
Compare the mean and s.d of the random sample to the population parameters.
The mean of the sample is less than population mean while the s.d. of the sample is greater than the population s.d.
22.86
6.36x
Sample
x
S
25.1
5.3 x
Population
Example 2For a large population, the mean = 4.8 and the s.d =3.6.
One random sample produced the following data values: 5, 1, 3, 4, 7, 6, 8, 2, 1, 3.
Compare the means and s.d’s of the random samples to the population parameters.
The mean and standard deviation of the sample are less than population mean and the population s.d.
1
4
2.45x
Sample
x
S
4.8
3.6 x
Population
Example 3For a large population, the mean = 12.3 and the s.d =4.24.
One random sample produced data values of
21, 13, 15, 12, 20, 22, 16, 18.
Another random sample produced data values of
14, 15, 12, 20, 29, 18.
Compare the means and s.d’s of the random samples to the population parameters.
The mean of the both samples are greater than population mean. The s.d. of the 1st sample is less than that of the population s.d while the s.d. of the 2nd sample is greater than the population s.d.
1
17.13
3.72x
Sample
x
S
2
18
6.10x
Sample
x
S
12.3
4.24 x
Population
Example 4: Compare Statistics and Parameters
less than
greater thanless than
17.8
12.35x
Gillian
x
S
21.1
14.52x
Ted
x
S
18.4
15.6 x
Population
Example 5: Compare Statistics and Parameters
A teacher wants to know how often her students study at night. Random samples are collected from John and Sally, two students. Their results are given below. The population mean is 1.24 and the population standard deviation is about 2.32. Compare the means and standard deviations of the random samples to the populations parameters. John: .35, 1.23, .55, 2, 3.1
Sally: 1.1, .46, 2.3, .25, 2.2
1.45
1.13x
John
x
S
1.26
0.96 x
Sally
x
S
1.24
2.32 x
Population
The mean of the both samples are greater than population mean. The standard deviations of both samples are less than that of the population standard deviation.
ComparingA Population and A Sample
A population is a group of people or objects that you want information about • “ the whole”, everything or everyone which is
relevant
A sample is a subset of the population • “the part”, just a piece of the population
Example: ECHS student survey • sample = 1 student from each class
• population = all the students in the school
Example: Each week, the Gallup Poll questions about
1500 adult US residents to determine
national opinion on a wide variety of issues.
What is the population?
Population = all US residents that week Who is the sample?
Sample = 1500 US residents questioned
Random Sample A sample in which each member of the
population has an equal chance of being selected.
Examples: Putting everyone’s name in a hat and pulling one out. Having a computer randomly generate a list of items.
Representative samples
A principal wants to know if teachers would be willing to give $1.00 each week to help provide new text books for the students. Which would give a representative sample?
A) Ask teachers who have first period planning
B) Ask the teachers that want new text books in their classrooms
C) Ask teachers as they sign in each morning
Representative random samples
The following list provides the average number of cookies baked for a bake sale. A food inspector wants to choose samples of cookies to inspect. Choose a method of random selection that is representative of all cookies.
A) choose the first cookie baked by each person
B) choose at random, 2 cookies from each person
C) choose at random, 5 cookies from Joe, 3 cookies from Sally and 7 cookies from Jane
Joe 20
Sally 12
Jane 28
Representative random samples
The following list provides the average number of t-shirts made by a t-shirt company. The manager wants to choose samples of t-shirts to inspect. Choose a method of random selection that is representative of all t-shirts.
A) choose 5 black t-shirts, 10 white and 50 red
B) choose at random, 30 Black shirts, 25 White shirts and 20 Red shirts
C) choose at random, one of each shirt
Black 1500
White 1250
Red 1000
SamplesUnbiased vs. Biased
Unbiased (FAIR) Sample:
A representation of the population you want information about.
Biased Sample:
A sample that over represents the population or under represents part of the population.
Examples: 1. A pharmacy wants to find out if its customers
would be interested in ordering their prescription through their website.
Asking every third prescription customer if they would be interested would be an ______ sample.
2. A movie theater wants to know which day of the week its customers prefer to see movies.
A sample would be to ask the question to all of its customers on Thursday.
unbiased
biased
Examples: 3. A school is trying to find out what is the
favorite sport among the students.
Asking every other football player, “What is your favorite sport?” would be a sample.
4. A store wants to know which style of jeans customers prefer.
An sample would be to ask every other customer what their favorite style of jeans is.
biased
unbiased
Census Every individual in the population is
contacted• not really practical because they are very time
consuming and extremely costly. Example:
• the US does a census every 10 years. It tries to contact everyone in the US and asks them questions about race, ethnicity, # of people in their house hold, etc.
The next census will occur in 2020.
Assignment:
Pg. 275 # 6 – 8, 11 Pg. 276 # 1, 2, 4 – 6
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