What is the standard deviation of the following data set rounded to the nearest tenth? 3, 17, 18, 15, 12, 21, 9

The standard deviation of the data set is 5.7 to the nearest tenth

Step-by-step 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