CUET CUET General Test 2024 - 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 is 4 (p is a natural number), then the value of (k - 2p) is: | PYQs + Solutions

CUET General Test 2024

Arithmetic

Central Tendency

Medium

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 $6$ is $4$ (p is a natural number), then the value of $(k - 2p)$ is:

Correct Option: 3

Mean

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

\Rightarrow 46+3k = 64

\newline

\Rightarrow 3k = 18 \rightarrow k = 6

4

is the mode then

4

must have the maximum frequency in the given series.

This means that either

2p

2p+1

must be equal to 4.

\newline

Also, the question mentions that

p

is a natural number so

2p+1

can't be equal to 4.

\therefore 2p = 4 \rightarrow p=2

(k-2p) = 6-4=2