Median

Median is the value of the middle number in a given data. It is the value in which an observation is equal after dividing the distribution into two. It refers to the middle number in a set of data or distribution arranged in order of magnitude. Arrangement is in ascending or descending order.

Example 4.3.1:

Find the median of the following set of numbers 31, 48, 76, 66, 25, 55, 10

Solution:

Step 1: Rearrange in order of magnitude;

10, 25, 31, 48, 55, 66, 76

Step 2: Locate the number in the middle. If the number of observations is odd, the number in the middle of the list is the median.

There are 7 numbers (3 to the left and 3 to the right) so the number in the middle is the median.

10, 25, 31, 48, 55, 66, 76

The median = 48

Example 4.3.2:

Find the median of the following set of numbers 55, 14, 69, 97, 130, and 27

Solution:

Step 1: Rearrange 14, 27, 55, 69, 97, 130

Step 2: Locate the number in the middle. If the number of observations is even, the median is the simple average of the middle two numbers.

14, 27, 55, 69, 97, 130

Median is \( \frac{55 \:+ \:69}{2} \\ = \frac{124}{2}\\ = \scriptsize 62 \)

Advantages of Median:

1. It is very easy to compute.

2. The median does not require calculation. 

3. Solution can be obtained at a glance.

4. Median is a suitable average in any set of numbers.

5. It is useful to measure qualities.

Disadvantages of Median:

1. Median is not a very good measure for central tendency.

2. If large numbers are involved it may prove cumbersome.

3. The medium may not be required for further statistical work.

4. It is not a very reliable measure of average if a set of numbers has many figures or digits.

5. Median does not consider the values of other numbers.