Median

The median, in statistics, is the middle value of a given list of data when arranged in either ascending or descending order.

As an example, the median of the set $\left\{2,3,4\right\}$ is 3.

Finding the median

The median of a set of data is the middlemost number or the center value in the set. The median is also the number that is at the 50th percentile of the set.

To find the median, the data should be arranged first in order from least to greatest or greatest to least. A median is a number that is separated by the higher half of the data sample, a population, or a probability distribution from the lower half. The median is different for different types of distributions.

If there is an odd number of data points, the median will be the center data point.

Example 1:

Find the median for the following data:

$\left\{0.3,6.2,1.5,0.7,5.1,2.3,3.0\right\}$

The first job is to put the data in order from least to greatest. You could also put the data in order from greatest to least, but we'll use least to greatest here.

$\left\{0.3,0.7,1.5,2.3,3.0,5.1,6.2\right\}$

Now count that there are seven data points. So the median is the middle number, the fourth data point.

2.3 is the median of the above set of data.

If there is an even number of data points, the median will be the average of the values of the two center data points.

Example 2:

Find the median for the following data set:

$\left\{71,93,50,82,12,16,55,58\right\}$

First, put the data in order from least to greatest.

$\left\{12,16,50,55,58,71,82,93\right\}$

Now count that there are eight data points. The middle two are 55 and 58, the fourth and fifth numbers.

So the median is the average of these two numbers.

$\frac{(55+58)}{2}=\frac{113}{2}$

$=56.5$

So the median of the data set above is 56.5, even though it matches no data point in the list.

Practice questions on how to find the median

1. Find the median for the following data set:

$\left\{84,91,103,82,78,97,101,90,73,85,99\right\}$

First, put the data in order, this time from greatest to least

$\left\{103,101,99,97,91,90,85,84,82,78,73\right\}$

Count that there are eleven data points. So the median is the central data point, which is the sixth data point.

The median of the data set is 90.

2. Find the median for the following data set:

$\left\{104,132,129,115,138,109,122,135,118,104,114,108\right\}$

First, put the data in order from least to greatest. Note that there are two data points that are the same. This doesn't affect the search for the mean.

$\left\{104,104,108,109,114,115,118,122,129,132,135,138\right\}$

Count that there are twelve data points. The median will be the average of the two central data points, the sixth and the seventh.

$\frac{115+118}{2}=\frac{233}{2}=116.5$

The median of the data set is 116.5.

3. Find the median for the following data set:

$\left\{1.35,1.28,1.10,1.49,1.32,1.47,1.25,1.35,1.22,1.47,1.18,1.43,1.36\right\}$

First, put the numbers in order from least to greatest.

$\left\{1.10,1.18,1.22,1.25,1.28,1.32,1.35,1.35,1.36,1.43,1.47,1.47,1.49\right\}$

Count that there are 13 data points. The median will be the central data point, which is the seventh data point.

The median of the data set is 1.35.

It doesn't matter that there are two data points of 1.35. The central data point is 1.35, making 1.35 the median.

Topics related to the Median

Combinations

Mutually Exclusive Events

Standard Deviation

Flashcards covering the Median

Statistics Flashcards

Common Core: High School - Statistics and Probability Flashcards

Practice tests covering the Median

Probability Theory Practice Tests

Common Core: High School - Statistics and Probability Diagnostic Tests

Get help learning about the median

Learning to find the median can be confusing for students at first, because they may be more used to finding the average of a set of numbers. Finding the median may seem deceptively simple. If your student needs help learning to find the median in a list of data, having them work with a math tutor who has an understanding of this probability and statistics topic is a great idea.

A tutor can help your student work towards their math goals effectively using a plan that addresses their academic strengths, areas of opportunity, and goals. They can give your student continuous, in-the-moment feedback as they work on homework assignments, allowing them to do the work the right way from the beginning so bad habits don't form. If your student has any knowledge gaps that are preventing them from understanding how to find the mean of a set of data, their tutor can help them address these gaps and bring them up to speed.

A tutor will work with your student at their speed, taking extra time when needed for challenging material and working quickly through material your student understands easily. To learn more about how tutoring can benefit your student, contact the Educational Directors at Varsity Tutors today.