The median is the middle value when all data points are arranged in order from smallest to largest. Half the values lie above it and half below. For an even number of values, the median is the average of the two middle values.
If you lined up your whole class by height, the median height is the person standing exactly in the middle. It's not affected by whether the tallest kid is 5'5" or 7 feet - the middle person stays the same.
Showing a random 20 of 50 problems.
Example 1
medium
Find the median of the first ten positive integers 1,2,…,10.
Example 2
challenge
A set of 5 positive integers has median 4, and all values are distinct. What is the smallest possible sum?
Example 3
easy
Find the median of 0,3,6,9.
Example 4
medium
Find the median of 14,22,14,30,22,14.Six values — the median falls between the two middle values. Find it.
Example 5
easy
Fill in: for an odd number of sorted values, the median position is 2n+1. For n=7, the median is at position ____.
Example 6
medium
Find the median of 11,15,17,19,23,29,31.
Example 7
medium
Five home prices in $1000s: 250,260,280,300,2000. Which is a more honest 'typical' price, mean or median?
Example 8
hard
Why is the median often preferred to the mean for reporting income?
Example 9
medium
Three students score 80,90,x. Their median equals their mean. Find x.
Example 10
easy
Find the median of 2,6,4.
Example 11
challenge
Seven distinct positive integers have median 10 and mean 10. The largest is 20. What is the largest possible value of the third-smallest integer (i.e., position 3 in sorted order)?
Example 12
medium
If a data set has n=15 sorted values, the median is at position ____.
Example 13
medium
Compare mean and median: data set {2,3,4,5,100}. Which is closer to the bulk of the data?
Example 14
easy
Find the median of −2,0,5,7.
Example 15
hard
Five integers have median 10 and the smallest two are 3 and 5. What is the smallest possible value of the largest?
Example 16
medium
Find the median of the nine values 5,5,6,7,8,9,10,11,12.
Example 17
challenge
Seven distinct positive integers have median 10. What is the smallest possible value of their sum?
Example 18
medium
A data set is {4,7,9,x} with median 8. Find x if x>9.
Example 19
medium
Add a value to {2,4,6} so the median becomes 5. What value should be added?