Exercise 18 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=36+18+12+10+9/5

AddTerms

Add terms

Mean=85/5

CalcQuot

Calculate quotient

Mean=17

The mean is 17. 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
36	36-17= 19	19^2 = 361
18	18-17= 1	1^2=1
12	12-17= -5	( -5)^2=25
10	10-17= -7	( -7)^2 = 49
9	9-17= -8	( -8)^2=64

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

361+1+25+49+64/5

AddTerms

Add terms

500/5

CalcQuot

Calculate quotient

100

The final step is to find the square root of the mean of the squared deviations. sqrt(100)=10 The standard deviation of the data is 10.