Find the median of 8, 10, 19, 23, 26, 34, 40, 41, 41, 48, 51, 55, 70, 84, 91, 92.
(i) If we include one value to the data (in the given list) without affecting the median, what could that value be?
(ii) If we include two values to the data without affecting the median what could the two values be?
(iii) If we remove one value from the data without affecting the median what could the value be?

Question

Bright Tutorials · Accepted Answer

The given data set is 8, 10, 19, 23, 26, 34, 40, 41, 41, 48, 51, 55, 70, 84, 91, 92
The number of observations (n) = 16 (even)
Median = average of $\left(\frac{n}{2}\right)^{t h}$ and $\left(\frac{n}{2}+1\right)^{t h}$ terms
= average of 8th and 9th terms
= $\frac{41+41}{2}$
= $\frac {82}{2}$
= 41
(i) To keep the median 41 with an odd number of values (n = 17), the new value must be placed at the median itself in the order list for making the middle value the 9th value. So the value could be 41.
(ii) With n = 18 (even) the median is the average of the 9th and 10th values.
To keep the median 41, we need to add two numbers whose sum is 82.
For this, one value should be less than 41 and the other greater than 41.
For example, the two values could be 40 and 42.
(iii) With n = 15 (odd) the median is the 8th value that is 41.
So we can remove another 41 from the ordered list.

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