Find the standard deviation of the sample data set 127 135 128 131-133 127 122

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