lesson 5-8 pages 238-242 measures of central tendency lesson check 5-7
TRANSCRIPT
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Lesson 5-8 Pages 238-242
Measures of Central
TendencyLesson Check 5-7
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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.
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Measures of central tendencyMeasures of central tendency
MeanMean
MedianMedian
ModeMode
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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.
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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!
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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
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Example 1: Mean
601601
330330
461461
313313
431431
309309
400400
306306
357357
++ 290290
3,798
3,798 ÷ 10
379.8
$379.8 million
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290290 306306 309309 313313 330330 357357 400400 431431 461461 601601
Example 1: Median
330 + 357 = 687
687 ÷ 2 = 343.5
$343.5 million330330 357357
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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
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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.
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Example 2:
7 8 9 103 4 5 60 1 2 11 12 13 14
xx
xx
xx
xx
xx
xx
xx
xx
xx
xx
xx
xx
xx
xx
xxxx
xxxx
xxxx
xx xxxxxx
There are 24 numbers in this set of data!
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Example 2:
7 8 9 103 4 5 60 1 2 11 12 13 14
xx
xx
xx
xx
xx
xx
xx
xx
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
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Example 2:
7 8 9 103 4 5 60 1 2 11 12 13 14
xx
xx
xx
xx
xx
xx
xx
xx
xx
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69 ÷ 24 = 2.875 mean
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Example 2:
7 8 9 103 4 5 60 1 2 11 12 13 14
xx
xx
xx
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xx
xx
xx
xx
xx
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xx xxxxxx
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.
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Example 2:
7 8 9 103 4 5 60 1 2 11 12 13 14
xx
xx
xx
xx
xx
xx
xx
xx
xx
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The mode is 0
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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.
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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
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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?
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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
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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.
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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?
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Example 5:
146 • 4 = 584138 + 140 + 145 = 423584 – 423 = 161
Jenny needs to score at least 161 on her fourth game.
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Page 241
Guided Practice
#’s 3-9
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Pages 238-240 with someone at home and study
examples!
Read:
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Homework: Pages 241-242
#’s 10-16 all
#’s 21-35
Lesson Check 5-8
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Page
735
Lesson 5-8
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Lesson Check 5-8