Algebra 1 Common Core Student Edition, Grade 8-9

Go t I t? 2. a. The grades in Problem 2 were 80, 93, and 91. What grade would you need

on your next exam to have an average of 88 on the four exams?

b. Reasoning If 100 is the highest possible score on the fourth exam, is it

possible to raise your average to 92? Explain.

A measure of dispersion describes how dispersed, or spread out, the values in a data

set are. One measure of dispersion is range. The range of a set of data is the difference

between the greatest and least data values.

How do t he pur poses
of the range and the
mean di f f er?
The range helps you find
how spread out the data
values are. The mean
helps you find a typical
data value.

Problem 3 Fi n d i n g t h e Ra n g e

Fi n an c e The closing prices, in dollars, of two stocks for the first five days in February

are shown below. What are the range and mean of each set of data? Use the results to

compare the data sets.

Stock B: 34 28 31 36 31

range: 36 — 28 = 8

Stock A: 25 30 30 47 28

range: 47 - 25 = 22

mean: 25 + 30 + 30 + 47 + 28 mean:34 + 28 + 31 + 36 + 31

160

5 32 = ijp = 32

Both sets of stock prices have a mean of 32. The range of the prices for Stock A is 22, and

the range of the prices for Stock B is 8. Both stocks had the same average price during

the 5-day period, but the prices for Stock A were more spread out.

& Got It? 3. For the same days, the closing prices, in dollars, of Stock C were 7,4, 3,

6 , and 1. The closing prices, in dollars, of Stock D were 24,15, 2,10, and

5. What are the range and mean of each set of data? Use your results to
   compare Stock C with Stock D.

Why can
mult iplication be
used when finding
the mean?
Multiplication is
equivalent to repeated
addition. Rather than
adding 2 four times, you
can multiply 4 times 2.

Problem 4 Fi n d i n g M e a su r e s of Cen t r al Ten d en cy an d Ran g es

The results of a survey on the number of televisions in students’

households are shown in the line plot.

Q Calculate the mean, median, and range of the data.

(2 *1 )+ (4 • 2) + (6 • 3) + (4 • 4) + (2 • 5) 54

Mean: lg - w

Median: 1, 1, 2, 2, 2, 2, 3, 3 ,( 373 ^ 3 , 3 , 4 ; 4 , 4 , 4 , 5 , 5 ;

Range: 5-1=4

The mean is 3, the median is 3, and the range is 4.

0 How can you tell from the graph that the mean and median are equal?

When the graph is symmetric, the mean and median will be equal.

Tel ev i si o n s

per Household

X

X

XXX

XXX

X X X X X

X X X X X

1 2 3 4 5

740 Ch ap t e r 12 Data Analysis and Probability