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Median

The median of a set of observations is the middle most observation when the observations are
arranged in ascending or descending order. Look at the following pictures,

2 students Student in 2 students 3 students 2 student in 3 students
before the middle after before the middle after
Fig. (i) Fig. (ii)
Here, we can see that, in fig. (i), there is 1 middle position of object if the number of objects is
odd, and in fig. (ii), there are 2 middle positions of objects if the number of objects is even.

Thus, when the number of observations is odd, then the middle
observation is the median. Remember
When the number of observations is even, then the mean of two To find the median, first we
middle observations is the median. will have to rearrange the
observations into ascending
Example 15: Find the median of the following data: and descending order.
(a) 3, 7, 2, 0, 9, 8, 3, 4, 8
(b) 7, –2, –3, 3, 2, 0, 8, 6, 3, 4
Solution: (a) First arrange the observations in ascending order, we get 0, 2, 3, 3, 4, 7, 7, 8, 9

0, 2, 3, 3, 4, 7, 8, 8, 9
middle observation
Number of observations = 9 (odd) = median
Therefore, the middle observation, i.e., 4 is the median of the given data.
Thus, the required median is 4.
(b) First arrange the observations in ascending order, we get –3, –2, 0, 2, 3, 3, 4, 6, 7, 8

Number of observations = 10 (even)
33 6
+
Therefore, the mean of 2 middle observations = 2 = 2 = 3
Therefore, 3 is the median of the given data. –3, –2, 0, 2, 3, 3, 4, 6, 8, 7

Example 16: The weight (in kg) of 11 students of a Mean to 2 middle
class are: 37, 52, 32, 46, 36, 40, 53, 34, 49, 41, and 47 observations = median

Find the median weight.
Alternate Method
Solution: Arranging the weights is ascending order, If the number of observations is n (odd),
we get, 32, 34, 36, 37, 40, 41, 46, 47, 49, 52, 53  n +  1

Number of observations, n = 11 (odd) Then, median =   th observation

 2
+

Therefore, the median is the middle observation, i.e., 41. So, median =  11 1
 2   th observation
32, 34, 36, 37, 40, 41, 46, 47, 49, 52, 53  12
=  2   th observation

Median = middle term = 6th observation = 41
Thus, the required median weight is 41 kg. Thus, the required median weight is 41 kg.

Mathematics-7 314