Exercise 21 Page 312

There are four steps to follow when finding the standard deviation of a set of data.

1. Find the mean of the data.
2. Find the squared deviation of each data value.
3. Find the mean of the squared deviations.
4. Find the square root of the mean of the squared deviations.

Let's start by finding the mean, or average, of the data set from the exercise.

Mean=Sum of values/Number of values

SubstituteValues

Substitute values

Mean=13+14+18+13+12+17+15+12/8

AddTerms

Add terms

Mean=114/8

CalcQuot

Calculate quotient

Mean=14.25

The mean is 14.25. Now, we can find the deviation from the mean for each value and square it. Let's use a table to organize the information.

Data Value	Deviation from Mean	Squared Deviation
13	13-14.25= -1.25	( -1.25)^2 = 1.5625
14	14-14.25= -0.25	( -0.25)^2=0.0625
18	18-14.25= 3.75	( 3.75)^2=14.0625
13	13-14.25= -1.25	( -1.25)^2 = 1.5625
12	12-14.25= 2.25	2.25^2=5.0625
17	17-14.25= 2.75	2.75^2=7.5625
15	15-14.25= 0.75	0.75^2=0.5625
12	12-14.25= -2.25	( -2.25)^2=5.0625

Next, we can find the mean of the squared deviations.

1.5625+0.0625+14.0625+1.5625+5.0625+7.5625+0.5625+5.0625/8

AddTerms

Add terms

35.5/8

UseCalc

Use a calculator

4.4375

The final step is to find the square root of the mean of the squared deviations. sqrt(4.4375) ≈ 2.1 The standard deviation of the data is approximately 2.1.