Math Word Problems Demystified - A Self Teaching Guide

3. Square the answers:

ð
 5 Þ^2 ¼ 25

ð
 3 Þ^2 ¼ 9

02 ¼ 0

32 ¼ 9

52 ¼ 25

4. Find the sum of the squares:
   25 þ 9 þ 0 þ 9 þ 25 ¼ 68


5. Divide the sum byn
   1, wheren¼5 andn
   1=5
   1=4:
   68  4 ¼ 17


6. Find the square root of 17:
   ffiffiffiffiffi
   17

p

¼ 4 :12 (two decimal places)

The standard deviation is 4.12.

EVALUATION: The standard deviation can be estimated by dividing the
range by 4. In this case, the range is 10. Thus, 10 4 ¼2.5. Since this is only a
rough estimate, we are in the ball park.

Roughly speaking, most of the data values will usually fall between two
standard deviations of the mean.

Try These

For the data set 32, 25, 18, 18, and 17, find each:

1. The mean.


2. The median.


3. The mode.


4. The range.


5. The standard deviation.

SOLUTIONS:

1. 32þ 25 þ 18 þ 18 þ 17 ¼110 110 5 ¼22 Mean¼ 22

LESSON 23 Word Problems in Statistics 281