Math Word Problems Demystified - A Self Teaching Guide

STRATEGY: Subtract the smallest data value from the largest data value in

the set.

IMPLEMENTATION: The smallest data value is 8, and the largest data

value is 24, so the range is 24
 8 ¼16.

EVALUATION: Redo the problem.

The range is a rough estimate of variation, so statisticians also use what is

called the standard deviation. The standard deviation can be computed by

using the following procedure:

1. Find the mean for the data set.


2. Subtract the mean from each value in the data set.


3. Square the differences.


4. Find the sum of the squares.


5. Divide the sum byn
   1 wherenis the number of data values.


6. Take the square root of the answer. (You may need a calculator for
   this step.)
   EXAMPLE:Find the standard deviation: 10, 12, 15, 18, and 20.

SOLUTION:

GOAL: You are being asked to find the standard deviation for the given

data set.

STRATEGY: Use the procedure given.

IMPLEMENTATION:

1. Find the mean:
   10 þ 12 þ 15 þ 18 þ 20 ¼ 75
   75  5 ¼ 15


2. Subtract the mean from each data value:

10 
 15 ¼
 5

12 
 15 ¼
 3

15 
 15 ¼ 0

18 
 15 ¼ 3

20 
 15 ¼ 5

280 LESSON 23 Word Problems in Statistics