Practice Mean vs Median in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick 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.

Showing a random 20 of 50 problems.

Example 1

medium
Adding a value equal to the current mean to a data set leaves the mean unchanged. True or false?

Example 2

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

Example 3

easy
For left-skewed data, order the mean and median.

Example 4

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 5

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

Example 6

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

Example 7

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

Example 8

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 9

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

Example 10

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

Example 11

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 12

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

Example 13

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

Example 14

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

Example 15

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

Example 16

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 17

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

Example 18

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

Example 19

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 20

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