Mean Greater than Median

Introduction of Mean and Median:

Mean nothing but the average of the total value which denoted as x. To find mean value of given is defined as the ratio of the sum of given number divided by the total numbers. Median is middle number of set of data value after arranging the data as in ascending order. In this article, we see about the mean of the data value is greater than median of the data value with example problems.

Formula – to Find Mean and Median:

Mean = sum of data/ number of data in set.

Median:

Case 1: If the given set of value is in odd numbers, then we can arrange the data in ascending order and find the middle term.

Case 2: If the given set of value is in even numbers, then we can arrange the data in ascending order and find the mean value of the center two numbers. Is this topic Estimating Sample Size hard for you? Watch out for my coming posts.

Example Problem – Mean Greater than Median:

Example 1:

Check the mean value is greater than median value of the following data.

34, 21, 70, 45, 64, 12

Solution:

To find Mean Value:

Step 1:

Sum of the given set of data value is

34 + 21 + 70 + 45 + 64 + 12 = 246

Step 2: Count the given set data

Here there are 6 data given.

Step 3: Formula: sum of data/ number of data in set

Step 4: `(246)/(6)` = 41

Hence the mean value of the data is 41

Mean: 41

To find the median value:

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

12, 21, 34, 45, 64, 70

Step 2: Check the total number of data is odd or even. Here the given data are in even number.

Step 3: Find the middle number of given set of data.

Here 34 and 45 are the middle number.

Step 4: Find the mean value of the two numbers.

`(34+45)/(2)` = 39.5

That the median value of the given set of data is 36.5

Median: 39.5

Compare both mean and median value of the given set of data.

Mean: 41 and median: 39.5

41 > 39.5

Mean > median

Hence we concluded that the mean value is greater than the median value of the given set of data.

Example 2:

Mean value of the following data is 30.8 and check the mean is greater than median.

23, 17, 95, 4, 15

Solution:

To find median value:

Step 1:

Arrange the ascending order of given set of data.

4, 15, 17, 23, 95

Step 2: Check the total number of data is odd or even. Here the given data are in even number.

Here the given set is in odd number.

Step 3: Find the middle value of the given set of data in ascending form.

Here 17 is the middle number

Median: 17

Compare both mean and median value of the given set of data.

Mean: 30.8 and median: 17

30.8 > 17

Mean > median

Hence we concluded that the mean value is greater than the median value of the given set of data.