Difference Between Mean and Median
Mean and Median are two commonly used terms in mathematics, mean is like average of a given numbers and it sums up the numbers and divide them with the count of numbers which gives us the mean while median on other hand returns the middle number from the whole data set and if the data set is even then median adds the two middle numbers and divides it by 2 giving us the median.
They are the measure of central tendency and are often used in the measurement of large data sets where analysis needs to be drawn, and results are interpreted. Mean, median, and mode are three measures of averages that show the disperse the data is from the mean or the average. These methods are used in statistics widely, whereas the mean value of the data is the most widely used method among the three.
What is Mean?
Mean is a simple sum of the numbers of observations in an array, which is divided by the numbers of observations. For example, if we talk about the average height or the mean height of a group consisting of 5 people. The mean height would be calculated by summing the height of 5 people divided by the number of people, i.e., 5.
Formula
What is the Median?
Median, on the other hand, is the middle number in the set of the data array, which separates the higher set of the data from the lower. The data needs to be arranged in ascending order first to calculate the median of the data. When the data set have cardinality, the mean of the middle two numbers in the data set needs to be taken. However, these two methods are often used interchangeably.
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Formula
when n is an odd number
when n is an even number
Mean vs Median Infographics
Let’s see the top differences between mean vs median.
Mean vs Median Key Differences
- Mean is simple to use and apply and can be applied to any data array set, whether even or odd. Median, on the other hand, is slightly complex to use, and the data set needs to be arranged in the ascending or the descending order first before calculation.
- The mean is normally used for normal distributions, whereas the median is used for the skewed distributions data set.
- The mean is simple, but it is not robust become it can contain outliers in the distributions and can sometimes not give the user the correct results for interpretation. On the other hand, the median method is robust and is better suited to use for as it used for skewed distributions to derive the central tendency of the date set and will give the user many accurate results when compared to mean
- There is only one formula of mean that is the sum of all the observations divided by the numbers of observations. Whereas, the median has two formulas, one of the odd where just the middle numbers from the dataset become the median. But when we have even data set, the middle of the two values are picked and are divided by 2, which then gives us the median of the even data set.
Mean vs Median Comparative Table
Mean | Median | |
The mean is computed by adding up all the values in the data array, which is then divided by the numbers of observations. | Median is the exact middle value of the data set. It can be computed by arranging the data set in the ascending order and then finding or picking out the middle value from the data set. | |
It is more widely used in the industry due to an easy computation of the average, and it gives us a quick number. | It is not used often in the industry, but it is more complete and accurate than mean, which just a simple sum of numbers. | |
It is used generally for normally skewed data set, i.e., normal distribution. | It is particularly handy to describe the dataset with a significant skewness in the data or when the data has a long tail. It is used widely where the outliners carry significant weight in the data there mean is not a good method of calculation. | |
It is not a robust tool for a calculation to derive the central tendency. | It is a much robust tool as it determines the weight in the data, which is generally high weight at the longer tails. | |
It is very sensitive to outliers. | It is much less affected by the outliers. | |
It is simple to use | It is complex in nature. | |
It cannot be calculated for categorical data, as the values cannot be summed. | It cannot be identified for categorized nominal data as it cannot be logically ordered. |
Conclusion
Apart from the mean and median, there is one more method that is often used for measuring central tendency that is the mode. A mode is a value which is most frequently occurred in the data set; the mode has an advantage over the mean and median that it can be found for both numerical and categorized data sets.
Despite the existence of mode and median the superiority of better results and analysis over the mean, the mean is still the most appropriate measure of central tendency, especially if the data set is a normal distribution, and the data is normally skewed.
As a good analyst, the central tendency should be measured with all three data methods, and the variance in the analysis should be pondered and carefully analyzed to produce better and more accurate results in the data set.
Recommended Articles
This has been a guide to Mean vs Median. Here we discuss the top differences between them along with infographics and a comparison table. You may also have a look at the following articles –
- Calculate Weighted Mean
- Normal Distribution Graph Excel
- Variance and Standard Deviation
- Geometric Mean vs. Arithmetic Mean
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