Question 50

For a series of 5 numbers, the mean is 20, the median and mode are both 10, the highest number in the series is 50 and one of the numbers is 20. Find the number of times the modal value appears in the series.

Solution

If we arrange the five numbers in ascending order, median is 10, and fifth number is 50, thus series : x, y, 10, z, 50

Also, mean is 20, => $$\frac{x+y+10+z+50}{5}=20$$

=> $$x+y+z=100-60=40$$

Now, mode is 10, Case 1 : If $$x=10$$, then we can have $$y=z=15$$, and thus 10 cannot be mode.

Case 2 : If $$x=y=10$$, thus $$z=20$$, and mode is 10

Thus, modal value appears 3 times.

=> Ans - (D)

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