A sample of size n=10n=10 is drawn from a population. The data is shown below.138.8116.497114.2138.8100.4128.8138.8101.9117.6What is the range of this data set?range =What is the standard deviation of this data set? (Remember, it is a sample.) Please report the answer with appropriate rounding, rounding to two more decimal places than the original data. Please, please, please do not calculate the value by hand.stdev =
Accepted Solution
A:
Answer:The range of this data set is 41.8The standard deviation of the data set is 16.42Step-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