1. Check it out! 1.5.3: Estimating Sample Means
1.5.3: Estimating Sample Means

2. Weight training (hours)
A coach is analyzing his players’ weekly off-season exercise routines. He has gathered the following data, including each player’s age, the number of miles they run, and the number of hours spent weight training.
Player
Age (years)
Running (miles)
Weight training (hours)
Angel 15 40 2
Blake 17 25 5
Jaime 16 10 7
Pat 12
Rene 30 3
Common Core Georgia Performance Standards: MCC9–12.S.IC.4★
1.5.3: Estimating Sample Means

3. What is the mean age of this sample?
What is the mean of the miles spent running for this sample?
What is the mean of the hours spent weight training for this sample?
What is the standard deviation of the miles that were run for this data set to the nearest tenth?
1.5.3: Estimating Sample Means

4. What is the mean age of this sample?
In order to calculate the mean age of the players, first find the sum of the ages.
= 80
Then divide the sum by the number of quantities in the data set, 5.
80 ÷ 5 = 16
The mean of the sample ages is 16 years.
1.5.3: Estimating Sample Means

5. What is the mean of the miles spent running for this sample?
In order to calculate the mean of the miles run, first find the sum of the miles run.
= 105
Divide the sum by the number of quantities in our data set, 5.
105 ÷ 5 = 21
The mean of the miles run for this sample is 21 miles.
1.5.3: Estimating Sample Means

6. What is the mean of the hours spent weight training for this sample?
In order to calculate the mean of the hours spent weight training, first find the sum of the hours.
= 29
Divide the sum by the number of quantities in our data set, 5.
29 ÷ 5 = 5.8
The mean of the hours spent weight training for this sample is 5.8 hours.
1.5.3: Estimating Sample Means

7. The number of values in the data set, n, is 5.
What is the standard deviation of the miles that were run for this data set to the nearest tenth?
The standard deviation can be found using the formula , where n is the number of values in the data set, x is each value of the data set, and is the mean.
The number of values in the data set, n, is 5.
1.5.3: Estimating Sample Means

8. The value of the mean, , was determined to be 21.
The values of x include 40, 25, 10, 0, and 30. We can assign these values as follows: x1 = 40, x2 = 25, x3 = 10, x4 = 0, and x5 = 30.
The value of the mean, , was determined to be 21.
Formula for standard deviation
Substitute for 5 for n and 21 for .
Expand the summation as shown below.
1.5.3: Estimating Sample Means

9. Substitute 40 for x1, 25 for x2, 10 for x3, 0 for x4, and 30 for x5, as shown.
Simplify.
1.5.3: Estimating Sample Means

10. The standard deviation of miles that were run for this data set is approximately 14.3 miles.
Connection to the Lesson
Students will continue to work with mean and standard deviation and apply these calculations to sample populations.
1.5.3: Estimating Sample Means