Datacollection Median

Another measure of central tendency that is frequently used is the Median. A median is that value in the series of data, which divides it exactly into two equal parts when the data are arranged in ascending, or descending order. The median of raw data is calculated as follows

1. When the number n of observations is odd, the median is the value of the th observation.
2.  When the number n of observations is even, the median is the mean of the ()th and th observations

Example 14:

Find the median of the following data.

15, 35, 18, 26, 19, 25, 29, 20, 27

Solution:

First arrange the data in ascending order.

15, 18, 19, 20, 25, 26, 27, 29, 35

Here n = 9 an odd number. The median is the th number

= = 5th observation

5th observation = 25

The median is 25.

Example 15:

Find the median of the following data:

78, 56, 22, 34, 45, 54, 39, 68, 54, 84

Solution:

Rearranging the observation in ascending order

22, 34, 39, 45, 54, 54, 56, 68, 78, 84

Here n =10 an even number.    Median = Average of the th and th observation, that is the average of the = 5th The median is 54.

Example16:

The following data have been arranged in the ascending order of magnitude.

59, 62, 65, x, x + 2, 72, 85, 94

If the median of the data is 69, find the value of n.

Solution:

59, 62, 65, x, x + 2, 72, 85, 94

Number of observations = n = 8 which is an even number. Find the median of the following observations.

1. 15, 40, 25, 16, 28, 32, 36, 42, 16, 19, 28
2. 3, 18, 6, 16, 12, 10
3. 122, 127, 109, 118, 125, 108

1. 15, 40, 25, 16, 28, 32, 36, 42, 16, 19, 28
Rearranging in ascending order
15, 16, 16, 19, 25, 28, 28, 32, 36, 40, 42
n = 11 an odd number 2. 3, 18, 6, 16, 12, 10
Rearranging is ascending order
3, 6, 10, 12, 16, 18
n = 6, an even number 3. 122, 127, 109, 118, 125, 108
Rearranging is ascending order
108, 109, 118, 122, 125, 127
n = 6
As in the previous case 