If the mean of 3, 4, 9, 2k, 10, 8, 6 and (k + 6) is 8, and mode of 2, 2, 3, 2p, (2p+ 1), 4, 4, 5 and 6 (p is a natural number) is 4, then the value of (k-2p) is:

2

The correct answer is Option (3) → 2

According to the question,

The mean of 3, 4, 9, 2k, 10, 8, 6 and (k + 6) is 8, and mode of 2, 2, 3, 2p, (2p+ 1), 4, 4, 5 and 6 (p is a natural number) is 4

We know that,

Mean =  \(\frac{sum \;  of \;observation}{number\;of \;observation}\)

Mode = Maximum frequency of the data.

Now,

8 = \(\frac{3 + 4 + 9 + 2k + 10 + 8 + 6 + k + 6}{8}\)

64 = 46 + 3k

3k = 64 - 46

3k = 18

k = 6

Mode = Maximum frequency of the data, and it is given that the mode is 4. So the value of p must be 2 for the maximum frequency of the 4.

Put the value of k and p in (k-2p) = (6-2(2)) = 2