Is Median the Average ? Hence Proved – Maths
In previous post, we learned about the concept of average and where do we use average in maths and in our daily life. Today in this post our students are going to learn that is median the average? To answer this question must follow this post carefully.
Is Median the Same as Average
The average is the data’s mean value, which differs from the data’s median value. The median is the value in the middle of a set of data arranged in increasing order. A central tendency is another term for the median or middle value. To calculate the measure of central tendency, we must arrange the data points in ascending or descending order. Furthermore, the median calculation is affected by the number of data points. Therefore, No, the median is not regarded as the average. Let us prove it.
How to Calculate Median Value
Consider the following two scenarios for calculating the medians value.
Scenario 1: If n is odd. There will be only one middle data point and median of the data is the (n + 1)/2 observations.
Scenario 2: If n is even number. Then there will be two middle data points and the median will be the average of n/2 and (n/2 + 1) observation.
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In Special scenario, when the data points are evenly spaced, then the average is equal to the median.
Consider the following numbers: 6, 9, 15, 21 and 24. The sum of (6 +9 + 15 + 21 + 24) divided by 5 is the average of this data. As a result, the data’s average is 75/5 = 15. Its value is in the middle, and it is equal to 15. For this data, the average and medians are both 15.
How to Solve Medians Problems
Let us explain the solution by solving the problem. When you are asked to find the median value of 16, 58, 15, 59, 60.
In first step you will re-arrange the series in ascending order. Such as: 15,16,58,59,60
In second step, count how many numbers are there i.e. 5. So, 5 is an odd number.
In third step, use the formula as per scenario mentioned above. Here in this case we have odd number so we use scenario 1 formula. i.e. (n + 1)/2
= 5+1/2= 6\2= 3
It means our answer is 58, because it is place at 3rd number in the ascending series, which we had arranged in ascending order.
Similarly we use Scenario 2 formula as mentioned above, in case when there is n number is even.
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