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, representing the data’s midpoint. The median is often compared with other descriptive statistics, such as the mean (average), mode, and standard deviation.
Understanding
Median statistics is a branch of mathematics. It involves collecting and studying data, which allows researchers to make inferences or determinations about a topic. Quantitative data analysis can be used to study anything from demographics to populations to investments, among other things. A median is the middle number in a sorted list of numbers (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 are an odd number of numbers, the median value is the number in the middle, with the same number below and above.
- To determine the median value if the list contains even numbers, choose the middle pair, add them, and divide by two.
The median can be used to determine an approximate average or mean, but it should not be confused with the actual mean.
Median vs. Mean
As noted above, it’s important not to confuse median and mean. The two may sound the same (which is a common misconception), 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. 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, 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
Conversely, the median would be six or (5 + 7) ÷ 2. That’s because we add an even number of data points together and divide by 2 to get the result.
Example of a Median
To find the median value in a list with an odd number, one would find the number in the middle with an equal number of numbers on either side of the median. First, arrange the numbers to find the median, 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 number, 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?
The median is the middle value in a set of data. First, organize and order the data from smallest to largest. To find the midpoint value, divide the number of observations by two. If there are an odd number of observations, round that number up, and the value in that position is the median. If the number of observations is even, take the average of the values found above and below that position.
Where is the median in a normal distribution?
In the normal distribution or bell curve, the median, mean, and mode all have the same value and fall at the highest point in the center of the curve.
When are the mean and median different?
The mean and median will typically be different in a skewed data set. One can calculate the mean by adding up all the data values and dividing by the number of observations. If there are sizable outliers or the data clumps around specific values, the mean (average) will not be the data’s midpoint. For instance, in the set of data {0, 0, 0, 1, 1, 2, 10, 10}, the average would be 24/8 = 3. The median, however, would be 1 (the midpoint value). Many economists favor the median for reporting a nation’s income or wealth since it represents income distribution.
The Bottom Line The median is the number in the middle of an ordered dataset that goes from lowest to highest. It should not be confused with the mean, which is determined by adding the numbers in a set together and dividing them by the total number of data points. Many experts prefer using the median over the mean because it often provides a more accurate representation of the distribution in a data set.
Conclusion
- When you sort a list of numbers, the median is the number in the middle. It can tell you more about the set of numbers than the average.
- People sometimes use the median instead of the mean when values are very different from the set’s and could change the average.
- There are an odd number of numbers in a set. The median value is the number in the middle, with the same number of numbers below and above it.
- If the number of numbers in the list is even, you must find the middle pair, add them together, and then split them by two to get the median value.
