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Objective

Find the mean, median, and mode of a set of data

Vocabulary

Measures of Central Tendency

Used to describe the center of data

Most Common

Mean

Median

Mode

Vocabulary

Mean

The sum of the data divided by the number of items in the data set

Vocabulary

Median

The middle number of the ordered data (odd number of data set)

Or

The mean of the middle 2 numbers (even number of data set)

Vocabulary

Mode

The number(s) that occur most often

Example 1 Find the Mean

Example 2 Find the Mean, Median, and Mode

Example 3 Analyze Data

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ANIMALS The table below shows the number of species of animals found at 30 major zoos across the United States. Find the mean.

Source: The World Almanac

659300800400705400300300350232640435488347195400133350290800280715700700617175400283400300

Number of Species in Major U.S. Zoos

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Mean = sum of datapieces of data

659300800400705400300300350232640435488347195400133350290800280715700700617175400283400300

2,849 2,487 2,921 2,283 2,554

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Add the data in each column

Put sum of columns in equation

Mean = 2,849 + 2,487 + 2,921 + 2,283 + 2,554

Count the number of pieces of data and put in the denominator

30

Answer: Mean =

Mean =2,849 + 2,487 + 2,921 + 2,283 + 2,554

30

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Add the numerator

Mean = 13,09430

Bring down denominatorDivide

Mean = 436.466666. . .

SLEEP The table below shows the results of a survey of 15 middle school students concerning the number of hours of sleep they typically get each night. Find the mean.

Answer: Mean =

7 8 6 7 89 5 6 7 78 6 7 8 8

Nightly Hours of Sleep

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hours

OLYMPICS The table below shows the number of gold medals won by each country participating in the 2002 Winter Olympic games. Find the mean, median, and mode of the data.

Source: CBSSportsline.com

0000122011243211324610034612

2002 Winter Olympics: Gold Medals Won

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Mean = 35 + 15 +11 +11 +70000122011243211324610034612

25

7925

Mean = 3.16

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Add the data in each column

Count the pieces of data

Add the numeratorMean =

Bring down denominatorDivide

OLYMPICS The table below shows the number of gold medals won by each country participating in the 2002 Winter Olympic games. Find the mean, median, and mode of the data.

Source: CBSSportsline.com

0000122011243211324610034612

2002 Winter Olympics: Gold Medals Won

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Median: Place numbers in order from least to greatest (make sure you use all numbers

0000122011243211324610034612

0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 6, 6, 10, 11, 12

There are 25 numbers so find the middle number

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Divide 25 by 2 which is 12.5

The number not underlined is the median

Since 25 divided by 2 is 12.5 , use the whole number 12

0000122011243211324610034612

0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 6, 6, 10, 11, 12

Place a line under the first 12 numbers

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Place a line under the last 12 numbers

Median = 2

OLYMPICS The table below shows the number of gold medals won by each country participating in the 2002 Winter Olympic games. Find the mean, median, and mode of the data.

Source: CBSSportsline.com

0000122011243211324610034612

2002 Winter Olympics: Gold Medals Won

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Mode is the number appearing most often

Answer: mean = 3.06; median = 2; mode = 0

0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 6, 6, 10, 11, 12

Use list from median to find mode

6 5 Mode = 0

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With a visual inspection, notice there are many 0’s and 2’sCount how many of each

Note: If no number is listed more than once then the mode would be “none”

PETS The table below shows the number of pets students in an art class at Green Hills Middle School have at home. Find the mean, median, and mode of the data.

Answer: mean = 1.44; median = 1; mode = 0

0 2 1 0

1 3 5 2

0 1 0 2

3 1 2 0

Pets

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FIRST FAMILIES The line plot in the bottom margin shows the number of children of United States presidents. Would the mean, median, or mode best represent the number of children?

Must find the mean, median, and mode to know which would best represent the number of children

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Add the data in each column

Mean =

Multiply the number by how many “x”’s

0(7)+ 1(5)+ 2(11)+ 3(4)+ 4(6)+ 5(6)+ 6(3)+ 7(2)+ 8(1)+ 10(1)

Count total pieces of data and put in denominator

46

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Follow Order of Operations Rules

Mean =

P E MD AS

0(7)+ 1(5)+ 2(11)+ 3(4)+ 4(6)+ 5(6)+ 6(3)+ 7(2)+ 8(1)+ 10(1)

Must do operations in numerator before using denominator

46

Do all multiplication first

Mean = 0 + 5 + 22 + 12 + 24 + 30 + 18 + 14 + 8 + 10

Bring down the denominator

46

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Follow Order of Operations Rules

Mean =

P E MD AS

Add all numbers together in numerator

46

Mean =

0 + 5 + 22 + 12 + 24 + 30 + 18 + 14 + 8 + 10

46143

Bring down the denominator

Divide

Mean = 3.11

FIRST FAMILIES The line plot in the bottom margin shows the number of children of United States presidents. Would the mean, median, or mode best represent the number of children?

Must find the mean, median, and mode to know which would best represent the number of children

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Order numbers from least to greatest

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There are 7 zeros so must list it 7 times

0, 0, 0, 0, 0, 0, 0,

Do each of the other numbers the same way

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,

3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 10

3, 3,

Remember, when we found the mean there were 46 pieces of data so divide 46 by 2

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0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 10

which is 23

Note: There are no numbers left no underlined so find the mean of the two numbers in the middle

Underline the first 23 numbersUnderline the last 23 numbers

Median =2 + 32

Median = 2.5

FIRST FAMILIES The line plot in the bottom margin shows the number of children of United States presidents. Would the mean, median, or mode best represent the number of children?

Must find the mean, median, and mode to know which would best represent the number of children

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With a number plot, just look at the plot and find which number(s) have the most x’s

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Mode = 2

Answer: The mean and median are very close together so they both could best represent the number of children of US presidents

Mean = 3.11Median = 2.5

Mode = 2

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FIRST FAMILIES The line plot in the bottom margin shows the number of children of United States presidents. Would the mean, median, or mode best represent the number of children?

If there are no outliers, the mean is usually the best representation

In this case the median is very close to the mean and there are no outliers

SIBLINGS The line plot below shows the number of siblings of each student in a particular classroom. Would the mean, median, or mode best represent the number of siblings?

Answer: The mean, median, and mode are close with values of 1.56 (without the outlier), 2, and 2 respectively.

The median or mode would be best representative of the data

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Assignment Lesson 2:4 Mean, Median, Mode 10 - 16 All