Download Warm-Up

Lesson 4.2
Core Focus on
Ratios, Rates & Statistics
Measures of Center
Warm-Up
Evaluate.
9  16  12  15
1.
4
13
10  8  15
2.
3
11
3. Put the following numbers in order:
0, 4, 5 2 ,
16, 4, 9.5,
20
,
3
0, 5
1
2
1 20
,
3
9.5, 16
Lesson 4.2
Measures of Center
Find measures of center and range.
Vocabulary
Measures of Center
Three numbers which are commonly used to represent a set of
numbers. (Mean, Median and Mode)
Mean
The sum of all the values in a data set divided by the number of
values; also known as an average.
Median
When all the numbers have been put in order from least to greatest,
the median is the middle number of the ordered data set.
Mode
The number(s) or item(s) in a data set which occurs the most often.
Explore!
Counting Pets
The measures of center can be used to summarize the number of pets
that students own. Cameron asked eight of his classmates how many
pets they own. The results are listed below.
1, 0, 2, 0, 3, 7, 0, 2
Step 1 Cameron wants to know the average number of pets that
students own. The word “average” refers to the mean of the
data set. The mean is the sum of all the values divided by the
number of values.
a. Find the sum of all the pets in the list.
b. Divide the sum by the number of students Cameron asked.
This number represents the mean of the data.
Explore!
Counting Pets
Step 2 Another measure of center is called the median. When all the
numbers have been put in order from least to greatest, the
median is the middle number of the ordered data set.
a. Put the numbers in Cameron’s list in order from least to
greatest.
b. Because there are an even number of values in the data set,
there will be two middle numbers in the list. Count in from
each end to find the two middle numbers. What are they?
c. When there are two middle numbers, the median is found by
finding the mean of the two middle numbers. Add the two
middle numbers together and divide by two. This is the
median.
Explore!
Counting Pets
Step 3 The last measure of center is the mode. The mode is the
number(s) or item(s) in a data set which occurs the most often.
There can be one mode, no mode or multiple modes. What
number of pets showed up most often in Cameron’s data set?
This is the mode.
Step 4 If Cameron wants to convince his parents that they should get
another pet, which measure of center should he use? Explain
your choice.
Measures of Center
Mean
The sum of all
values divided by
the number of
values
Mean 
Sum of Values
Number of Values
Median
The middle
number of an
ordered data set
Mode
The number or
item in a data set
which appears
most often
If there are two
middle numbers,
find the mean of
those numbers.
A data set may
have one mode,
no mode or
several modes.
Example 1
Find the mean, median and mode for the following data sets:
Total numerator
a. 3, 8, 9, 9, 10, 10, 28
before dividing.
Find the mean.
The mean is 11.
3  8  9  9  10  10  28 77

 11
7
7
Find the median.
The median is 9.
3, 8, 9, 9, 10, 10, 28
Find the mode.
The modes are 9 and 10.
Both 9 and 10 appear twice.
Example 1 Continued…
Find the mean, median and mode for the following data sets:
b. 17, 8, 10, 15, 19, 2, 9, 12
Find the mean.
The mean is 11.5.
17  8  10  15  19  2  9  12 92

 11.5
8
8
Find the median. Order
the numbers from least to
greatest. Ten and twelve
are the middle numbers.
2, 8, 9, 10, 12, 15, 17, 19
Find the mean of these
numbers. The median is 11.
10  12
 11
2
Find the mode.
There is no mode.
No number appears more
than any other number.
Vocabulary
Range
The difference between the maximum (largest value) and minimum
(smallest value) values in a data set.
Range = Maximum - Minimum
The maximum is the largest number in the data set.
The minimum is the smallest number in the data set.
Example 2
Find the range of the following data sets.
a. 17, 29, 33, 34, 38, 42
b. 26, 37, 40, 33, 35, 38
a. The maximum is 42 and the minimum is 17.
Range = Maximum − Minimum
= 42 − 17
= 25
b. The maximum is 40 and the minimum is 26.
Range = Maximum − Minimum
= 40 − 26
= 14
Example 3
Use the range to find the missing value in each ordered data set.
a. 11, 13, 16, 20, 22, ___
The range is 19 and the
minimum is 11.
Add 19 to 11 to find the
maximum value.
The missing value is 30.
Range = 19
Range = Maximum – Minimum
19 = Maximum – 11
19 + 11 = 30
Think: What number
minus 11 is 19?
Example 3 Continued…
Use the range to find the missing value in each ordered data set.
b. ___ , 35, 40, 40, 41, 45, 52
The range is 25 and the
maximum is 52.
Subtract 25 from 52 to find
the minimum value.
The missing value is 27.
Range = 25
Range = Maximum – Minimum
25 = 52 – Minimum
52 – 25 = 27
Think: 52 minus what
number is 25?
Communication Prompt
Which measure of center do you think is the easiest to
find? Which is the most difficult to find? Explain.
Exit Problems
1. Find the mean, median and mode of the following data set.
20, 32, 24, 40, 24, 28
Mean = 28; median = 26; mode = 24
2. Give an example of a data set with more than one mode.
0, 1, 3, 3, 4, 5, 6, 6, 7
3. What is the range of the data set?
82, 77, 85, 92, 89, 99, 79, 85
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