Question

in a perfectly symmetrical distribution the mode and mean are 42 and 49 respectively the approximate a median of this distribution is

Answer 1

We know that in a perfectly symmetrical distribution, the mean and the median are the same.  And if the data is unimodal then the mode will be the same as mean and median.

A perfectly symmetrical distribution is a distribution of a data set in a manner such that if a vertical line is drawn at some point in the histogram the shape to the left and the right of the vertical line are mirror images of each other

Here in our question value of the mode of the data set is 42 and the value of the mean of the data set is 49.  

Since the mean and median of a perfectly symmetrical distribution is the same, therefore, the approximate median of this distribution is 49.