Is defined as the value of the middle observation when the observations are arranged in the order of their magnitude?

The difference between mean and median is explained in detail here. In statistics, mean is the average of a set of data and the median is the middle value of the arranged set of data. Both values have their own importance and play a distinct role in data collection and organisation. Let us see what are other differences between them with the help of definitions, table and example.

Definition of Mean and Median

Mean: Mathematically. the mean can simply be defined as the list of numbers that are used to describe a central tendency. The method to calculate mean is simple enough, the variables need to be added and divided by the number of items in the overall sample. Assume a data value, say x1, x2, … , xn

So, the formula for calculating the mean is given as:

Mean =  (x1+ x2+ … + xn)/n

Here “n” is the total number of sample items.

Median: Median, on the other hand, can simply be defined as the number that is found in the middle of the set. Median is an essential quantity that can be used for separating the available sample into two; the higher half sample, as well as the lower half sample, can be procured in this method.

To proceed with the process of finding the median of the given data, first, arrange the given set of numbers on the ascending order, and then determine the middle value from the centre of the distribution. This condition can be suitable if we have an odd number of observations. But, in case of even number of observation, there is no single median value. So, in this case, add the two numbers in the middle and then divide it by 2. The obtained value is taken as a median value.

Here, the major difference between mean and median is listed below. Go through the following differences.

Thus, these are the major differences between Mean and Median. It is essential to know the major differences between the two.

Solved Example

Question: Find the mean and median for the following data:

3, 5, 4, 1, 8, 6, 9

Solution:

Given Data: 3, 5, 4, 1, 8, 6, 9

No. of. data = 7

The mean for the following data is given as:

Mean =  (3 +5 + 4 + 1 + 8 + 6 + 9)/7

Mean = 36/7 = 5. 14

Therefore, the mean of the following data is 5. 14

To find median:

Step 1: Arrange the given set of data in ascending order

So, it becomes: 1, 3, 4, 5, 6, 8, 9

Step 2: Since the number of data is odd, take the middle value

So, the middle value of the given data is 5.

Thus, the median value is 5.

Video Lesson on Median of Data

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