Question

If the median of 24, 27, 28, 31, 34, x, 37, 40, 42, 45 arranged in ascending order, is 35. Find the value of x. If the data 45 is changed to 33, find the new median.

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

We know the formula to find median is:

Firstly arranging the data in ascending order. After that checking if the number of data is odd or even.

If it is odd then the middle term is the median else if it is even then the average of value at the (n/2)th and (n/2)+1 th position is the median.

The data given here is: 24, 27, 28, 31, 34, x, 37, 40, 42, 45.

The no.of observations = 10 which is even.

So, median = avg of value at (n/2)th and (n/2)+1 th position

i.e. (34 + x)/2 = 35

or, 34 + x = 70

or, x = 36.

Now after changing the data 45 to 33,

We have: 24, 27, 28, 31, 33, 34, 36, 37, 40, 42

The new median will be: (33 + 34)/2 = 33.5 [Ans]