Answer:
The standard deviation of the sample data set is 4.36
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 122 , 127 , 127 , 128 , 131 , 133 , 135
∵ Their sum = 122 + 127 + 127 + 128 + 131 + 133 + 135 = 903
∵ They are seven
∴ The mean = 903 ÷ 7 = 13.29
# Step 2: subtract the mean from each data and square the answer
∴ (122 - 129)² = 49
∴ (127 - 129)² = 4
∴ (127 - 129)² = 4
∴ (128 - 129)² = 1
∴ (131 - 129)² = 4
∴ (133 - 129)² = 16
∴ (135 - 129)² = 36
# Step 3: find the mean of these squared difference
∵ The data is a sample data set
∵ The mean = the sum of the data ÷ (the number of the data - 1)
∵ The sum = 49 + 4 + 4 + 1 + 4 + 16 + 36 = 114
∴ The mean = 114 ÷ (7 - 1) = 114 ÷ 6 = 19
# Step 4: the standard deviation is the square root of this mean
∴ The standard deviation = √(19) = 4.3589 ≅ 4.36
* The standard deviation of the sample data set is 4.36
