Math Statistics: Median

The following diagrams show how to obtain the median from a given set of data. Scroll down the page for examples and solutions.

Steps to Find the Median

1. Arrange the Data:
   Sort the dataset in ascending or descending order.
   
2. Determine the Number of Data Points:
   Count the total number of data points (n).
   
3. Find the Median:
   If n is odd, the median is the middle value in the ordered dataset.
   If n is even, the median is the average of the two middle values.
   

Examples:
There are 2 possible cases to consider in finding the median.

Case 1. When the number of observations is odd, the median is the middle value.

Example:
Find the median of the following set of points in a game:
15, 14, 10, 8, 12, 8, 16

Solution:
First arrange the point values in an ascending order (or descending order).
8, 8, 10, 12, 14, 15, 16

The number of point values is 7, an odd number. Hence, the median is the value in the middle position.

Median = 12

Case 2. When the number of observations is even, the median is the average of the two middle values.

Example:
Find the median of the following set of points:
15, 14, 10, 8, 12, 8, 16, 13

Solution:
First arrange the point values in an ascending order (or descending order).
8, 8, 10, 12, 13, 14, 15, 16

The number of point values is 8, an even number. Hence the median is the average (mean) of the 2 middle values.

Given a partial data set, you may need to determine the possible values of the median of a set of numbers.

Example:
x is the median for 4, 3, 8, x and 7. Find the possible values for x.

Solution:
Arrange the numbers in ascending order with x in the middle.
3, 4, x, 7, 8

This tells us that the possible values of x are 4, 5, 6 and 7.

Statistics Worksheets
Practice your statistics skills with the following worksheets:
Statistics Worksheets
Median worksheets

The following videos will show you how to find the median.

How To Find The Median?

In this lesson you learn how to find the median from a set of numbers using the median position formula (n+1)/2.

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Mean Median And Mode

Example:
Find the mean, median and mode of the following set of data:
23, 29, 20, 32, 23, 21, 33, 25

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Mean, Median, Mode Song

A song to help you remember how to calculate mean, median and mode.

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SAT: Mean, Median, Mode

In the SAT, mean, median and mode questions may be given in the following manner.

SAT Mean, Median, and Mode Math Question

This video will show you how to answer SAT mean, median, and mode math questions.

In a set of nine distinct numbers which of the following cannot affect the median
a) squaring
b) increasing every other number by 5
c) increasing the smallest number only
d) increasing the largest number only
e) decreasing the largest number only

In a certain Chemistry class, the median score on a test was 84. Which of the following must be true?
I. The highest score in the class is at least one point higher than the lowest score.
II. If there was a score of 83 in the class, there was also a score of 85.
III. The mode of the test scores was 84.

If w, x and y represent 3 positive numbers where x = y + 5 and y = w + 20, what is the result when the average of the three numbers is subtracted from the median?
a) -5
b) 0
c) 4
d) 5
e) 15

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SAT Math - Averages, Median, List of Real Numbers

The least and greatest numbers in a list of 7 real numbers are 2 and 20, respectively. The median of the list is 6, and the number 3 occurs most often in the list. Which of the following could be the average (arithmetic mean) of the numbers in the list?
I. 1
II. 8, 5
III. 10

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Median
Use the median when:

• The dataset has outliers or is skewed.
  
• You want a measure of central tendency that is not influenced by extreme values.
  Comparison with Mean:
  
• The mean is the average of all values, while the median is the middle value.
  

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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