Average value of the median of 2, 8, 3, 7, 4, 6, 1 and the mode of 2, 9, 3, 4, 9, 6, 9 is:

1. 6

2. 6.5

3. 8

4. 9

Arranging set of observations in ascending order : 1, 2, 3, 4, 6, 7, 8

Here, n = 7, which is odd.

By formula,

Median = $\dfrac{\text{n} + 1}{2} \text{ th observation}$

$= \dfrac{7 + 1}{2} \text{ th observation} \\[1em] = \dfrac{8}{2} \text{ th observation} \\[1em] = 4 \text{ th observation} \\[1em] = 4$

Given,

2, 9, 3, 4, 9, 6, 9

From above set of numbers : 9 occurs most of the time.

Mode = 9.

Average of median and mode = $\dfrac{9 + 4}{2} = \dfrac{13}{2}$ = 6.5

Hence, Option 2 is the correct option.