What Is the Median?
The term median refers to a metric used in statistics. It is the middle number in a sorted ascending or descending list of numbers and can be more descriptive of that data set than the average. It is the point above and below which half (50%) of the observed data falls, and so represents the midpoint of the data. The median is often compared with other descriptive statistics such as the mean (average), mode, and standard deviation.
Key Takeaways
- The median is the middle number in a sorted list of numbers and can be more descriptive of that data set than the average.
- The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values.
- If there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above.
- If there is an even amount of numbers in the list, the middle pair must be determined, added together, and divided by two to find the median value.
Understanding the Median
Statistics is a branch of mathematics. It involves the collection and study of data, which allows researchers to make inferences or determinations about a certain topic. The analysis of quantitative data can be used to study anything from demographics, populations, and investments among other things.
A median is the middle number in a sorted list of numbers (either ascending or descending) used in statistical studies. To determine the median value in a sequence of numbers, the numbers must first be sorted or arranged in value order from lowest to highest or highest to lowest.- If there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above.
- If there is an even amount of numbers in the list, the middle pair must be determined, added together, and divided by two to find the median value.
The median can be used to determine an approximate average, or mean, but is not to be confused with the actual mean.
The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values. The median of a sequence can be less affected by outliers than the mean.
Median vs. Mean
As noted above, it's important not to confuse the terms median and mean. The two may sound the same, but they are very different. A median is a number that falls in the middle of a group. Remember, this is done by ordering the numbers from smallest to largest and locating the one that falls in the middle. A mean, on the other hand, is the average of a data set. Also called the arithmetic mean, it is the average of the sum of the numbers in a group. In order to figure out the mean, you must take the sum of the numbers in the group and divide the sum by the total number of data points. For instance, let's say a data set consists of the numbers 3, 5, 7, and 19. To figure out the mean:- Add the numbers together: 3 + 5 + 7 + 19 = 34
- Divide the sum by the number of data points: 34 ÷ 4 = 8.5
The median is closely associated with quartiles, or dividing up observed data into four equal parts. The median would be the center point, with the first two quartiles falling below it and the second two above it. Other ways of bucketing data include quintiles (in five sections) and deciles (in 10 sections).
Example of a Median
To find the median value in a list with an odd amount of numbers, one would find the number that is in the middle with an equal amount of numbers on either side of the median. To find the median, first arrange the numbers in order, usually from lowest to highest. For example, in a data set of {3, 13, 2, 34, 11, 26, 47}, the sorted order becomes {2, 3, 11, 13, 26, 34, 47}. The median is the number in the middle {2, 3, 11, 13, 26, 34, 47}, which in this instance is 13 since there are three numbers on either side. To find the median value in a list with an even amount of numbers, one must determine the middle pair, add them, and divide by two. Again, arrange the numbers in order from lowest to highest.For example, in a data set of {3, 13, 2, 34, 11, 17, 27, 47}, the sorted order becomes {2, 3, 11, 13, 17, 27, 34, 47}. The median is the average of the two numbers in the middle {2, 3, 11, 13, 17, 26 34, 47}, which in this case is 15 or (13 + 17) ÷ 2 = 15.
How Do You Calculate the Median?
Where Is the Median in a Normal Distribution?
In the normal distribution or bell curve the median, mean, and mode are all the same value and fall at the highest point in the center of the curve.