Question

If mode of a data is 45, mean is 27, then median is,
(a) 30
(b) 27
(c) 33
(d) None

Answer 1

Hint: To solve this question we first need to know the relation between mean, median and mode. For any given data it is certain that Mode = 3 Median – 2 Mean. So in the given question we are already given the mode and mean of a data and we have to find its median so we will directly put the values of mode and mean in the mentioned formula and then solve it to get the value of median.

Complete step by step answer:
We are given that mode of a data is 45 and for same data its mean is 27,
So to solve this we have to know the relation between mean, median and mode of a data,
For a given data we have,
Mode = 3 Median – 2 Mean.
We already have the values of mode and mean given as 45 and 27 respectively so we will put these values in the above expression to get the value of median, this we will do as,
Putting the Mode = 45 and Mean = 27, we get
45 = 3 Median – 2 $\times $ 27
45 = 3 Median – 54
Rearranging the terms we get,
3 Median = 45 + 54
3 Median = 99
Dividing both sides with 3, we get
Median = $\dfrac{99}{3}$
Median = 33
Hence we get median as 33 so option (c) is the correct answer.


Note:
To solve this problem you need to have the prior knowledge about the relation between the mean, median and mode of a given set of data otherwise without data it would not be possible for you to find anyone of them if the rest two are given. The very common mistake that students make while appearing for exams is that they write the formula as Mode = 2 Median – 3 Mean in a hurry and this will cost them the marks. So, do not rush, recollect and write the correct formula.