MATH SOLVE

4 months ago

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

Accepted Solution

A:

Answer:The standard deviation of the data set is 5.7 to the nearest tenthStep-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