Mean, Median and Mode

Mean, Median and Mode

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Mean, Median, Mode and Range are common ways we use statistics to describe a data set

They all tell us something different about a data group

The Range of a list of numbers is just the difference between the largest and smallest value

**To find the range, subtract the smallest value from the largest value

Example: What is the range of the following data set?:

1, 20, 3, 8, 5, 21

Range = 21-1

Range = 20

Multiple Choice

Find the range of the data.

63, 71, 65, 66, 87, 53

• 32

• 33

• 34

• 35

Multiple Choice

What is the range of miniature golf scores?

• 44 points

• 29 points

• 33 points

• 39 points

Mean is the average 

(sometimes written x̄)

We find the mean by adding all the data points and dividing by the total number of data points

Example: What is the mean of the following data set?:

2,6,8,4,9,10

Add the data points: 2+6+8+4+9+10= 39

And divide by the number of data points: 39/6

The mean (average) is 6.5

Multiple Choice

What is the definition of the mean?

• The average

• The middle number

• The difference between the highest and lowest numbers

• The number that occurs the most

Multiple Choice

What is a common symbol for mean?

• x

• x̄

• $$\sqrt{ }$$

• $$\sum_x^y$$

Multiple Choice

Find the mean:

28, 18, 19, 18, 17

• 20

• 18

• 11

• 19

The median is the middle number

We find the middle number but putting the data points in order

Example: What is the median of the following data set?:

21,13,14,16,18,13,13,13,14

Put the numbers in order and find the middle number:

13,13,13,13,14,14,16,18,21

The median is 14

Median continued...

What do you do if there is no "middle number" ?(even number of data points)

Find the average of the two middle numbers

Example: What is the median of the data set?

1,3,4,6,8,10

Find the average of the two middle numbers. The average of 4 and 6 is 5. Therefore, 5 is the median

Multiple Choice

Find the median:

5, 6, 3, 9, 0, 4, 1, 2, 7

• 4

• 4.1

• 5

• 4.5

Multiple Choice

Find the median:

3, 5, 7, 4, 3, 1

• 3 and 4

• There isn't one

• 3.5

• 3

The Mode is the number that is repeated more often than any other

Example: What is the mode of the following data set?

1,1,2,2,5,5,5,8,9

5 is repeated 3 times to it is the mode of the data set

**You can have more than one mode. For example, in the following data set is considered "bi-modal" because it has 2 modes:

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

The mode is 3 and 5

Multiple Choice

Can there be more than one mode?

• Yes

• No

Multiple Choice

Find the mode:

5, 0, 9, 9, 3, 0, 5, 5, 4

• 9

• 5

• 3

• 7

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A bar chart is a common way to show the relative size of data.

Multiple Choice

Which of the following statements is true?

• banana is the most popular fruit

• only pineapple is liked less than oranges

• kiwi is the most popular fruit

• apple is the third most popular fruit

Multiple Choice

In total, how many children take a taxi or cycle to school?

• 5

• 35

• 20

• 15

Multiple Choice

How many more children walk than take a taxi to school?

• 45

• 20

• 25

• 35

A histogram is like a bar chart but it groups data points into ranges

• So a tree that is 260 cm tall is added to the "250-300" range.

Multiple Choice

How many cities have temperatures between 70 degrees and 99 degrees?

• 44
• 34
• 26
• 62

Multiple Choice

Which interval shows the greatest number of pets?

• 15-19
• 0-4
• 5-9
• 10-14

Multiple Choice

How many students were greater than or equal to 60 inches tall?

• 21
• 11
• 17
• 6

Multiple Choice

What is the MEAN for this data?

• 80
• 1040
• 13
• 81

Multiple Choice

What is the MEDIAN of this data?

• 65
• 40
• 915
• 13

Multiple Choice

What is the MODE of this data?

• 90
• 85, 90, and 95
• 85 and 95
• None

Multiple Choice

What is the range of the test scores?

• 15
• 100
• 6
• 10

Multiple Choice

How many students received a score in the 80's?

• 2
• 10
• 14
• 27

Multiple Choice

How many students received a score of 94%? 

• 94
• 4
• 1
• 2

Multiple Choice

What is the highest score in the class?

• 88%
• 100%
• 13
• 98%