Mean vs Median Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Mean vs Median.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

Mean and median are both measures of center but respond differently to extreme values (outliers). The mean is pulled toward outliers because it uses every value in its calculation, while the median is resistant to outliers because it depends only on the middle position.

Imagine a room with 10 people earning \$50,000 each. Mean and median are both \$50,000. Now a billionaire walks in. Mean jumps to \$91 million! But median stays around \$50,000. Mean is a pushover that gets bullied by extremes; median stands firm.

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How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Mean vs Median asks what single value best stands for the center of the data, then checks whether that value is fair for the situation.

Common stuck point: Students often know a procedure related to mean vs median but skip the recognition step: Do I need one number that represents the center of the data, and have I checked whether extreme values change that choice? That leads to a calculation or graph that looks reasonable but answers a different question.

Sense of Study hint: Ask: Do I need one number that represents the center of the data, and have I checked whether extreme values change that choice?

Worked Examples

Example 1

medium
House prices (in thousands): 180,200,210,220,950180, 200, 210, 220, 950. Which measure better represents a typical home, and why?

Answer

median=210\text{median}=210

First step

1
Mean =(180+200+210+220+950)/5=1760/5=352=(180+200+210+220+950)/5=1760/5=352.

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Example 2

medium
A class of 10 has mean test score 7272. The teacher discovers one score should be 9090 instead of 00. What is the new mean?

Example 3

medium
Rents in a neighborhood (in $): 900,1000,1100,1200,4000900, 1000, 1100, 1200, 4000. Which is a fairer description of a typical rent and why?

Example 4

hard
Four numbers have mean 2020 and median 1818. The two middle values are 1515 and 2121. Find a possible value of the smallest and largest.

Example 5

hard
Test scores: 60,70,75,80,85,90,9560, 70, 75, 80, 85, 90, 95. The teacher curves by adding 55 to every score. What are the new mean and median?

Example 6

challenge
A reporter writes: 'Average household income in the town is \$120k, so most families do well.' The median is \$58k. Explain the misleading claim.

Example 7

medium
House prices on a street (in thousands): 200, 210, 190, 205, 195, 800. Calculate the mean and median. Which better represents a typical house price?

Example 8

medium
Test scores: 78, 82, 79, 81, 80. Calculate both the mean and median. What do you notice?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
For 2,3,42, 3, 4, find both mean and median.

Example 2

easy
For 1,2,301, 2, 30, which is larger, mean or median?

Example 3

easy
For 5,6,7,8,1005, 6, 7, 8, 100, find the median.

Example 4

easy
For 5,6,7,8,1005, 6, 7, 8, 100, find the mean.

Example 5

easy
Which measure better represents typical income in a town with one billionaire?

Example 6

easy
For symmetric data 10,20,3010, 20, 30, do mean and median agree?

Example 7

easy
For 1,1,1,1,961, 1, 1, 1, 96, find the median.

Example 8

easy
For 1,1,1,1,961, 1, 1, 1, 96, find the mean.

Example 9

medium
For 4,8,8,12,1004, 8, 8, 12, 100, compute mean and median and state which is more typical.

Example 10

medium
Data is right-skewed. Order the mean and median.

Example 11

medium
A set 4,5,6,x4, 5, 6, x has equal mean and median. The median is 5.55.5. Find xx.

Example 12

medium
Replacing the largest value 5050 with 500500 in a data set, what happens to mean vs median?

Example 13

medium
For 3,3,4,103, 3, 4, 10, by how much does the mean exceed the median?

Example 14

medium
A class median is 8080 but mean is 7272. What does this suggest about the scores?

Example 15

medium
For {2,4,6,8}\{2, 4, 6, 8\} replace 88 with a value vv so the mean equals the median. Find vv.

Example 16

challenge
Five distinct positive integers have mean 1010 and median 1010. Maximize the largest value.

Example 17

challenge
Show that adding a value equal to the current mean leaves the mean unchanged.

Example 18

challenge
A data set's mean equals its median equals its mode, all =7=7. Give the smallest such set of 33 distinct-count integers.

Example 19

medium
For 2,2,3,132, 2, 3, 13, find both the mean and the median.

Example 20

medium
A house-price list is right-skewed. Which center should a buyer trust as typical?

Example 21

easy
For 6,7,8,9,106, 7, 8, 9, 10, find the mean.

Example 22

easy
For 6,7,8,9,106, 7, 8, 9, 10, find the median.

Example 23

easy
For 2,4,6,82, 4, 6, 8, find the median.

Example 24

easy
For 2,4,6,82, 4, 6, 8, find the mean.

Example 25

easy
Five test scores: 70,75,80,85,9070, 75, 80, 85, 90. Find the median.

Example 26

medium
A set {3,7,8,x}\{3, 7, 8, x\} has mean 77. Find xx.

Example 27

medium
For 2,5,5,8,10,122, 5, 5, 8, 10, 12, find the median.

Example 28

medium
For 2,5,5,8,10,122, 5, 5, 8, 10, 12, find the mean.

Example 29

medium
Ten employees earn $30k\$30k each and the CEO earns $1,000k\$1{,}000k. Find the median salary.

Example 30

medium
Ten employees earn $30k\$30k each and the CEO earns $1,000k\$1{,}000k. Find the mean salary.

Example 31

medium
For 1,2,3,4,5,61, 2, 3, 4, 5, 6, find both mean and median.

Example 32

hard
A data set has 7 values with median 1212. If the largest value is replaced with one twice as large, what happens to the median?

Example 33

hard
Set {2,4,6,8,x}\{2, 4, 6, 8, x\} has mean 77. Find xx and the median.

Example 34

hard
A data set has mean 5050. If every value is increased by 77, find the new mean.

Example 35

challenge
A set of five positive integers has mean 66, median 77, and a unique mode 99. Find the smallest possible value of the largest element.

Example 36

medium
Salaries at a small company: \$30k, \$32k, \$35k, \$33k, \$31k, \$150k. Should the company report the mean or median salary to represent a typical employee's pay? Justify.

Example 37

medium
A runner's practice times (in minutes) are 24, 25, 24, 26, 25, 24. Would the mean or the median better describe a typical practice time? Explain.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

mean fair sharemedian introoutlier detection