Question

for an ungrouped data 10,15,20,25,15,x median and mode are equal.find x and also mean for the givendata

Answer 1

Mode is the most frequently occurred data. Without consider x, the mode is should be 15. x cannot be any value that already appear in the rest of the data (10, 20 or 25) and it is because if x is 10, 20 or 25, the data set will have dual mode (two modes) and it will not be equal to median. So the mode must be 15.

So what is the value for x? Let's check the median.

Median is the middle value of the data. Before we can find the median, we need to arrange the numbers in the right order (like below).

10, 15, 15, 20, 25

Since we know that mode is 15, in order to maintain median to be 15 too, x need be smaller than or equal to 15 so the data can line up like this

x, 10, 15, 15, 20, 25
10, x, 15, 15, 20, 25

So  $x \leq 15$ (but cannot be 10)

In this case, I don't think you can find the mean for this set of data as we are not sure of the value of x.