Median

We have seen that in some situations, arithmetic mean is an appropriate measure of central tendency whereas in some other situations, mode is the appropriate measure of central tendency.

Let us now look at another example.

Consider a group of 17 students with the following heights (in cm). Divide the class into two groups so that each group has equal number of students, one group has students with height lesser than or equal to a particular height and the other group has students with heights greater than or equal to the particular height.

How would you do that? Go ahead. Try. It's hard, right?

Let us see the various options you have:

(i) She can find the mean. The mean is.

Instruction

106 + 110 + 123 + 125 + 117 + 120 + 112 + 115 + 110 + 120 + 115 + 102 + 115 + 115 + 109 + 115 + 101 17 = 193017 = 113.5103

So, if the teacher divides the students into two groups on the basis of this mean height, such that one group has students of height less than the mean height and the other group has students with height more than the mean height.

Go ahead, divide the students into two groups on the basis of this mean height, such that one group has students of height less than the mean height and the other group has students with height more than the mean height, then the groups would be of unequal size.

They would have and members respectively.

(ii) The second option you have is to find mode. The observation with highest frequency is 115113 cm, which would be taken as mode. Go ahead and now re distribute the above based on mode.

There are children below the mode and children at the mode and above the mode. Therefore, we cannot divide the group into equal parts.

Let us therefore think of an alternative representative value or measure of central tendency.

For doing this we again look at the given heights (in cm) of students and arrange them in ascending order. We have the following observations:

101, 102, 106, 109, 110, 110, 112, 115, 115, 115, 115, 115, 117, 120, 120, 123, 125

The middle value in this data is because this value divides the students into two equal groups of 8 students each.

This value is called as Median. Median refers to the value which lies in the middle of the data (when arranged in an increasing or decreasing order) with half of the observations above it and the other half below it.

Here, we consider only those cases where number of observations is odd.

Thus, in a given data, arranged in ascending or descending order, the median gives us the middle observation.

Thus we realise that mean, mode and median are the numbers that are the representative values of a group of observations or data. They lie between the minimum and maximum values of the data. They are also called the measures of the central tendency.

Find the median of the data: 24, 36, 46, 17, 18, 25, 35

Can you arrange the data in ascending order?

Median is the middle observation. Therefore is the median.

Your friend found the median and the mode of a given data. Describe and correct your friends error if any:42,35, 32, 34,35, 38, 32

Can you arrange the data in ascending order and find the median and mode?

What is the Median :

What is the Mode :