Question

the median of the data set is 81 what number is missing in data set 82, 87, 77, 70, 80, 88

Answer 1

the number that missing is clearly 81

Answer 2

The missing dataset is 81 at the 4th position.

We have the following data set -

82, 87, 77, 70, 80, 88

whose Median is -  81

We have to find out the missing data in this dataset.

What is the formula to find the Median of a set of odd number of elements (say N) ?

If a set consist of odd number of elements, then the median of that set of numbers is the is the element at the position $(\frac{N+1}{2}) ^{th}$.

Let the missing element be x. Now, the data set becomes -

82, 87, 77, 70, 80, 88, x

To total number of elements in the dataset = 7, which is a odd number.

The element at the $(\frac{N+1}{2}) ^{th}$ position for odd number of elements equals to Median which is equal to 81.

Hence, the missing dataset is 81 at the position -    $(\frac{7+1}{2}) ^{th} = \frac{8}{2}$ = 4th position.

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