Bellwork August Copy and answer.

The data shows the ages of some dirt bike riders in an AMA Supercross Race. Put them in order from least to greatest.

17, 17, 19, 21, 22, 30, 19, 18, 19, 27, 29, 29, 16, 20

1. Make a stem-and-leaf plot of the data. How many riders are over the age of 20?

2. Make a line plot of the data. What age occurs most

often?

Unit 1Chapter 7Section 2Pg. 381

Mean, Median, Mode, and Rangewith and without Outliers

Essential Questions:• How does finding the measure of

central tendency help in analyzing data?

• What is central tendency?

Mean, Mode, and Median

http://www.youtube.com/watch?v=FDzwnoXZQZY

Definitions

mean: the average number of the set of datamedian: the middle number in a set of data after the numbers are arranged in order from least to greatest

mode: the number that occurs the most in a set of data

range: the difference between the highest and lowest numbers in the set of data

Definitions continued…

outlier: a number that is much smaller or much larger than the set of data

35, 38, 27, 12, 30, 41, 31, 35

10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42

xx xxxx xx xx xx xxxx

Vocabulary Study List (see your handout)

Vocabulary Word Keyword Picture Definition

mean the average number of a set of data

median the middle number after the numbers are arranged in order from smallest to largest

mode the number that occurs the most in a set of data

range the difference between the highest and lowest numbers in a set of data

outlier A number that is much smaller or larger than the other numbers in a set of data

Babe Ruth Central Tendency and Variability Video Clip (3:45)http://player.discoveryeducation.com/index.cfm?guidAssetId=a87b1f07-3e9e-4934-a26d-18125db4ea72

Write down 3 facts about Central Tendency.

Range!How to find the range:

1. Arrange the numbers in ascending order

2. Pick out the smallest number and the largest number.

3. Subtract the two numbers.

Example 1:

1, 2, 2, 2, 4, 4, 7, 8

– 1 = 8 7

Find the range of the data set.

4, 7, 8, 2, 1, 2, 4, 2

•MEAN

ACTIVITY 1

• Using interlocking number cubes, make 3 towers. – 6– 4– 8

• Now, figure out how to make them all the same length.

Activity 1, ctd.

• If you moved two cubes from the tallest tower and added them to the smallest tower, now how long are all three towers?

• 6• This is the MEAN. The mean of {8, 4, 6} is 6.

Activity 2

• Let’s find Mean another way. • Data Set { 1, 3, 5, 9}• Use interlocking cubes to make a tower for

each number.

Activity 2, ctd.

• Step 1: Find the SUM• Combine all the cubes from all the towers to add.• How many are their total?

• Step 2: Divide• There were originally 4 towers, so divide the cubes into

four EQUAL groups.• How many cubes are in each group?

– This is your MEAN.

How do you find the mean?1. Add all the numbers together to

get the sum

2. Divide the sum by the number of items in the data set.

Mr. GrumpyToday’s Assignment:

Find the mean of:2, 7, 9, 15, 12

SIT DOWN! GET QUIET!NO GUM!ZERO FOR YOU!

Example 2: Find the mean of the following data set.

6, 4, 3, 5, 2, 5, 1, 8

6 + 4 + 3 + 5 + 2 + 5 + 1 + 8 =

8 items sum

34

34 4.25 = 8

Mean Practice

• Complete the ‘No Rest for the Weary’ WS

• Show all work on a separate sheet of paper.

•MODE

How to find the mode?

Search to find the number that occurs the most. Sometimes it could be more than one number.

Example 3:

Find the mode of the data set.

4, 7, 8, 2, 1, 2, 4, 2

1, 2, 2, 2, 4, 4, 7, 8

Activity 3

• Name Lengths/Singers of Bands• Using the worksheet provided by your

teacher, we will cut strips of paper and fold them in half to represent the MEDIAN.

How to find the median?1. Arrange the numbers in order from least to greatest.2. Count until you find the middle number. If you have one number, then you have found the answer. If you have two numbers, then continue to step 3.

3. Add the two numbers together, then divide by 2 Median or

middle of the street

Example 4: Find the median of the data set.

4, 7, 8, 2, 1, 2, 4, 2

1, 2, 2, 2, 4, 4, 7, 8

2 + 4 = 6

6 2 = 3

Example 5:Find the median of the following data set.

6, 4, 3, 5, 2, 5, 1, 8

1, 2, 3, 4, 5, 5, 6, 8

4 + 5 = 9

9 2 = 4.5

Mean, Median, and ModeBrain-Pop

Write down 2 facts about mean, median, and mode from the clip.

Work Session• Find the mean, median, and mode for each

problem on the handout.• Show all work.• Remember the following:

– Mean: add up all of the numbers and divide them by how ever many numbers are in the data set

– Median: put the numbers in order from least to greatest and then find the number in the middle

– Mode: the number that occurs the most

Example 6: (Word Problem)The line plot shows the number of dollars each of the 10 members of the cheerleading team raised in a week. Which measure of central tendency best describes this data? Justify your answer.

10 20 30 40 50 60 70

XXXX

XXX

XXX

15 + 15 + 15 + 15 + 20 + 20 + 40 + 60 + 60 + 70

10

330 10

= 33=

Most of the cheerleaders raised less than $33, so the mean does not describe the data set.

The median is 20. The median best describes the data set because it is closest to the amount most cheerleaders raised.

The mode is 15. The mode focuses on one data value and does not describe the data set.

Outliers (9:56)http://player.discoveryeducation.com/index.cfm?guidAssetId

=4D5934D9-3890-4983-A918-11B91F11C2AA&blnFromSearch=1&productcode=US

Write down 3 facts about outliers.

Example 7: The data shows Sara’s scores for the last 5 math tests: 88, 90, 55, 94, and 89. Identify the outlier in the data set. Then determine how the outlier affects the mean, median, and mode of the data. Then tell which measure of central tendency best describes the data with the outlier.

outlier 5555, 88, 89, 90, 94

55+88+89+90+94= 416

416 5 = 83.2

The mean is 83.2.

55, 88, 89, 90, 94

The median is 89.

There is no mode.

mean: median: mode:

With the Outlier

Example 7:The data shows Sara’s scores for the last 5 math tests: 88, 90, 55, 94, and 89. Identify the outlier in the data set. Then determine how the outlier affects the mean, median, and mode of the data. Then tell which measure of central tendency best describes the data with the outlier.

outlier 5555, 88, 89, 90, 94

88+89+90+94 = 361

361 4 = 90.25

The mean is 90.25.

88, 89, 90, 94

The median is 89.5.

There is no mode.

mean: median: mode:

+2

= 89.5

Without the Outlier

Compare data with & without data

With the Outlier

The mean is 83.2. The median is 89.

There is no mode.

Without the Outlier

The mean is 90.25. The median is 89.5.

There is no mode.

The mean between the two are 7.05. The median changes .5. Taking out the outlier only changes the mean dramatically.

Possible Activities

• See the next few slides

Mean, Median, Mode, Range and Outliers with M&Ms

• Open your bag of M&Ms.

• Count how many M&Ms are in your bag (DO NOT EAT ANY YET)

• We will compare how many M&Ms are in the bags of of your classmates.

• Fill in your chart.

Person # of M&M’s in Their Bag

•Find the mean, median, and mode of the number of M&Ms in the bags.•Are there any outliers?•What is the range?