Lesson 5-8 Pages 238-242

Measures of Central

TendencyLesson Check 5-7

What you will learn!1. How to find the mean,

median, and mode as measures of central tendency.

2. How to use the mean, median, and mode.

Measures of central tendencyMeasures of central tendency

MeanMean

MedianMedian

ModeMode

What you really need to know!

When working with numerical data, it is often helpful to use one or more numbers to represent the whole set. These numbers are called measures of central tendency.

StatisticStatistic DefinitionDefinition

MeanMeansum of the data divided sum of the data divided by the number of items by the number of items in the setin the set

MedianMedian middle number of the middle number of the ordered setordered set

ModeMode number or numbers that number or numbers that occur most oftenoccur most often

What you really need to know!

Example 1:

The revenue of the 10 highest grossing movies as of June 2000 are given in the table. Find the mean, median, and mode of the revenues.

Top 10 Movie Top 10 Movie RevenuesRevenues

(millions of $)(millions of $)

601601 330330

461461 313313

431431 309309

400400 306306

357357 290290

Example 1: Mean

601601

330330

461461

313313

431431

309309

400400

306306

357357

++ 290290

3,798

3,798 ÷ 10

379.8

$379.8 million

290290 306306 309309 313313 330330 357357 400400 431431 461461 601601

Example 1: Median

330 + 357 = 687

687 ÷ 2 = 343.5

$343.5 million330330 357357

Example 1: Mode No Mode

This is no number or numbers that appear more than any other number. Therefore there is no mode.

290290 306306 309309 313313 330330 357357 400400 431431 461461 601601

Example 2:

The line plot on the next screen shows the number of gold medals earned by each country that participated in the 1998 Winter Olympic Games in Nagano, Japan. Find the Mean, median, and mode for the gold medals won.

Example 2:

7 8 9 103 4 5 60 1 2 11 12 13 14

xx

xx

xx

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xx xxxxxx

There are 24 numbers in this set of data!

Example 2:

7 8 9 103 4 5 60 1 2 11 12 13 14

xx

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xx xxxxxx

0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 1 + 1 + 2 + 2 + 2 + 2 +3 + 3 + 5 + 5 + 6 + 6 + 9 +

10 + 12 = 69

Example 2:

7 8 9 103 4 5 60 1 2 11 12 13 14

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69 ÷ 24 = 2.875 mean

Example 2:

7 8 9 103 4 5 60 1 2 11 12 13 14

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The numbers are all ready in order. Since there are 24 numbers, the median would be 12 from the top and bottom of the line plot.

The median is 2.

Example 2:

7 8 9 103 4 5 60 1 2 11 12 13 14

xx

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xx xxxxxx

The mode is 0

Example 3:

The quiz scores for a math class are 8, 7, 6, 10, 8, 8, 9, 8, 7, 9, 8, 0, and 10. Identify an extreme value and describe how it affects the mean.

Example 3:

0 is an extreme value.Mean with 0 is 7.5

Mean without 0 is 8.2

The 0 lowers the mean by 0.7 points.

0 6 7 7 8 8 8 8 8 9 9 10 10

Example 4:

The table shows the monthly salaries of the employees at two bookstores. Find the mean, median, and mode for each set of data. Based on the averages, which bookstore pays its employees better?

Bob’s BooksBob’s Books The Reading The Reading PlacePlace

12901290 14001400

14001400 14501450

14001400 15501550

16001600 16001600

36503650 20002000

9340 9340 ÷ 5÷ 5 8000 8000 ÷ 5÷ 5

$1868$1868 $1600$1600

Median MedianMode

Bob’s Bob’s BooksBooks

The The Reading Reading

PlacePlace

MeanMean $1,868$1,868 $1,600$1,600

MedianMedian $1,400$1,400 $1,550$1,550

ModeMode $1,400$1,400 No ModeNo Mode

The Reading Place pays its employees better.

Example 5:

Jenny’s bowling average is 146. Today she bowled 138, 140, and 145. What does she need to score on her fourth game to maintain her average?

Example 5:

146 • 4 = 584138 + 140 + 145 = 423584 – 423 = 161

Jenny needs to score at least 161 on her fourth game.

Page 241

Guided Practice

#’s 3-9

Pages 238-240 with someone at home and study

examples!

Read:

Homework: Pages 241-242

#’s 10-16 all

#’s 21-35

Lesson Check 5-8

Page

735

Lesson 5-8

Lesson Check 5-8