Asample of size n=10n=10 is drawn from a population. the data is shown below.

138.8

116.4

97

114.2

138.8

100.4

128.8

138.8

101.9

117.6

what is the range of this data set?

range =

what is the standard deviation of this data set? (remember, it is a sample.) report the answer with appropriate rounding, rounding to two more decimal places than the original data. , , do not calculate the value by hand.

stdev =

The range of this data set is 41.8

The standard deviation of the data set is 16.42

Step-by-step explanation:

* Lets read the information and use it to solve the problem

- There is a sample of size n = 10,  is drawn from a population

- The data are: 97 , 100.4 , 101.9 , 114.2 , 116.4 , 117.6 , 128.8 , 138.8 ,

  138.8 , 138.8

- The range is the difference between the largest number and

  the smallest number

∵ The largest number is 138.8

∵ The smallest number is 97

∴ The range = 138.8 - 97 = 41.8

* The range of this data set is 41.8

- Lets explain how to find the standard deviation

# Step 1: find the mean of the data set

∵ The mean = the sum of the data ÷ the number of the data

∵ The data set is 97 , 100.4 , 101.9 , 114.2 , 116.4 , 117.6 , 128.8 , 138.8 ,

  138.8 , 138.8

∵ Their sum = 97 + 100.4 + 101.9 + 114.2 + 116.4 + 117.6 + 128.8 + 138.8 +

  138.8 + 138.8 = 1192.7

∵ n = 10  

∴ The mean = 1192.7 ÷ 10 = 119.27

# Step 2: subtract the mean from each data and square the answer

∴ (97 - 119.27)² = 495.95

∴ (100.4 - 119.27)² = 356.08

∴ (101.9 - 119.27)² = 301.72

∴ (114.2 - 119.27)² = 25.70

∴ (116.4 - 119.27)² = 8.24

∴ (117.6 - 119.27)² = 2.79

∴ (128.8 - 119.27)² = 90.82

∴ (138.8 - 119.27)² = 381.42

∴ (138.8 - 119.27)² = 381.42

∴ (138.8 - 119.27)² = 381.42

# Step 3: find the mean of these squared difference

∵ A Sample: divide by n - 1 when calculating standard deviation of

  a sample

∵ The mean = the sum of the data ÷ (the number of the data - 1)

∵ The sum = 495.95 + 356.08 + 301.72 + 25.70 + 8.24 + 2.79 + 90.82 +

   381.42 + 381.42 + 381.42 = 2425.56

∴ The mean = 2425.56 ÷ (10 - 1) = 269.51

# Step 4: the standard deviation is the square root of this mean

∴ The standard deviation = √(269.51) = 16.416658 ≅ 16.42

* The standard deviation of the data set is 16.42