Question

If the median of 17,26,60,45 and 33 is 33 and if 17 is replaced by 27 then what will be the new median?

Answer 1

Hint: In the given question we are given the median of some given numbers. Now, we are being asked to find the median of a new set of numbers after replacing one number from the previous set of numbers itself. Median is the middle number of the set of numbers when arranged in ascending order.

Complete step-by-step solution:
According to the given question, the median of some set of numbers 17,26,60,45 and 33 is given to be 33. Now we are being asked to replace one number from these sets of numbers, that is we need to replace 17 by 27 and then we are asked to find the median of these sets of numbers.
Now, initially in order to find the median of the set of numbers we need to arrange them in ascending order which is 26,27,33,45,60.
Now, we can see that in total we have five numbers therefore, the position of the middle number would be $\dfrac{n+1}{2}$ where n=5 therefore, the number at 3rd place from left would be the middle number.
Therefore, the middle number is 33.
Hence, we can say that the median of the new set of numbers is 33.

Note: In these types of questions, we mostly forget to arrange the set of numbers in ascending order and directly write the middle number which gives us the wrong answer. Therefore, we need to be careful about this. Also, in case of even numbers we need to write the median properly.