Answer:
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
