Mean, Median Mode, Range, IQR Lesson

Measures of Center & Spread

Mean

"Average" of a set of numbers

​To calculate it:

1. Add up all the numbers in the data set.

2. Divide ​that total by the amount of numbers in the data set.

Mean Examples

Multiple Choice

Find the mean of these numbers:

2, 57, 38, 42, 6

• 29

• 38

• 50

• 145

Multiple Choice

Find the mean for these test scores:

67, 74, 95, 98, 98, 99, 102

• 90.4

• 633

• 98

• 92.3

Median

"Middle" number of a sorted list of numbers

​To calculate it:

1. Write the numbers in order from least to greatest.

2. Find the middle number.

3. If there are 2 "middle" numbers, the median will be the mean of those 2 numbers.

Median Examples

Multiple Choice

Find the median from the list of numbers:

60, 58, 52, 48, 60

• 58

• 59

• 60

• 118

Multiple Choice

What is the median of this set of data?
10, 90, 80, 60, 50, 40, 70, 30, 20, 100

• 50
• 60
• 55
• 45

Range

Difference between the largest & smallest values

in a set

​To calculate it:

1. Write the numbers in order from least to greatest.

2. Subtract (range = largest value – smallest value)

Range Example

Multiple Choice

Find the range.
12, 5, 9, 18, 22, 25, 5

• 20
• 15
• 22
• 18

Multiple Choice

Find the range of the data.

16, 28, 6, 19, 21, 15, 22, 33, 17

• 18

• 27

• 30

• 12

Quartiles

Divides the data in 4 equal parts

• 1st Quartile (Q1): the middle of the lower half of the data set

​

• 3rd Quartile (Q3): the middle of the upper half of the data set

Quartile Examples

Multiple Choice

Find the 1st Quartile (Q1) of the following data set:

2, 3, 4, 5, 5, 5, 7

• 4

• 6

• 3

• 5

Multiple Choice

Find the 3rd Quartile (Q3) of these numbers:

2, 3, 4, 5, 5, 5, 7

• 4

• 6

• 3

• 5

Interquartile Range (IQR)

Middle 50% of values when ordered from lowest to highest

​To calculate it:

1. Put the numbers in order from least to greatest.

2. Find the median.

3. Find the median of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3).

4. Find the difference between Q3 and Q1. (IQR = Q3 – Q1)

IQR Example

Multiple Choice

Find the IQR of the data.

20, 22, 25, 29, 31

• 30

• 21

• 25

• 9