Question

If the mode of some observations is 10 and the sum of the mean and median is 25, then the mean and median, respectively, are ______.

Options

• 12 and 13

• 13 and 12

• 10 and 15

• 15 and 10

Answer 1

If the mode of some observations is 10 and the sum of the mean and median is 25, then the mean and median, respectively, are 13 and 12.

Explanation:

Given, Mode = 10

Mean + Median = 25  ....(i)

We know that,

Mode = 3 Median – 2 Median

10 = 3(25 − Mean) − 2 Mean   ....[Fom equation (i)]

10 = 75 − 3 Mean − 2 Mean

5 Mean = 65

Mean = `65/5`

Mean = 13

Put the value of Mean in the equation (i).

Mean + Median = 25

13 + Median = 25

Median = 25 − 13

Median = 12