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Median of Grouped Data

a) The median is the middle of a distribution: One half of the scores are above the median and the other half below the median. The median is less sensitive to extreme scores than the mean and this makes it a better measure than the mean for highly skewed distributions. The mean, median, and mode are equal in symmetric distributions.

b) If the values of xi in a raw data are arranged in ascending or descending order, then the middle-most value in the arrangement is called the median.

c) Arrange the values in ascending or descending order of magnitude.

For computation of median of a ungrouped data, proceed as follows:

1. Take the middle-most value of the arrangement as the median.

2. If the number of values (n) in the raw data is odd, then the median will be the th value of the arrangement.


3. If the number of values (n) in the raw data is even, then the average of two middle most values th and th will determine the median.

The arithmetic mean of these two values will give the exact median.


Find the median of the following values of a variate:
10, 2, 3, 2, 5, 7, 9, 11, 6


Arranging the values in the ascending order. We get:
2, 2, 3, 5, 6, 7, 9, 10, 11
Here number of observations 
n = 9 (odd)

Median = size of the th term

Median = size of the th term
             = size of the 5th term = 6.

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