Answer:
The standard deviation of the data set is 5.7 to the nearest tenth
Explanation:
* 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 3 , 17 , 18 , 15 , 12 , 21 , 9
∵ Their sum = 3 + 17 + 18 + 15 + 12 + 21 + 9 = 95
∵ They are seven
∴ The mean = 95 ÷ 7 = 13.6
# Step 2: subtract the mean from each data and square the answer
∴ (3 - 13.6)² = 112.36
∴ (17 - 13.6)² = 11.56
∴ (18 - 13.6)² = 19.36
∴ (15 - 13.6)² = 1.96
∴ (12 - 13.6)² = 2.56
∴ (21 - 13.6)² = 54.76
∴ (9 - 13.6)² = 21.16
# Step 3: find the mean of these squared difference
∵ The mean = the sum of the data ÷ the number of the data
∵ The sum = 112.36 + 11.56 + 19.36 + 1.96 + 2.56 + 54.76 + 21.16 = 223.72
∴ The mean = 223.72 ÷ 7 = 31.96
# Step 4: the standard deviation is the square root of this mean
∴ The standard deviation = √(31.96) = 5.6533 ≅ 5.7
* The standard deviation of the data set is 5.7 to the nearest tenth