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

$\Rightarrow 46+3k = 64$

$\Rightarrow 3k = 18 \rightarrow k = 6$

If $4$ is the mode then $4$ must have the maximum frequency in the given series.

This means that either $2p$ or $2p+1$ must be equal to 4.

Also, the question mentions that $p$ is a natural number so $2p+1$ can't be equal to 4.

$\therefore 2p = 4 \rightarrow p=2$

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

2022: 17 Aug Shift 1

The median of data in numerals is

2022: 17 Aug Shift 1

The average of 3 odd consecutive numbers is 15. What is the sum of first and last numbers?

2025: 13 May Shift 2

The average of $39$ numbers is $17$ . Each number is multiplied by $12$ and then $16$ is added to each number. Finally, each number thus formed is divided by $11$ .

Determine the average of the new sets of numbers thus formed ?

2026: 14 May Shift 1

The A.M.(Arithmetic Mean) and G.M (Geometric Mean) of two positive numbers p and q are 8 and 4 respectively, then the value of p - q are

2025: 29 May Shift 1

The median and mean of 7 observations are 9 and 11 respectively. If 2 is subtracted from each observation, then the new median and the new mean will respectively be which of the following?

2026: 6 June Shift 1

If the median of x/5, x/4, x/2, x and x/3, where x > 0, is 8, find the value of x.

If the mean of 3,4,9,2k,10,8,63, 4, 9, 2k, 10, 8, 63,4,9,2k,10,8,6 and (k+6)(k + 6)(k+6) is 888, and mode of 2,2,3,2p,(2p+1),4,4,52, 2, 3, 2p, (2p + 1), 4, 4, 52,2,3,2p,(2p+1),4,4,5 and 666 is 444 (p is a natural number), then the value of (k−2p)(k - 2p)(k−2p) is:

Solution

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CUET General Test Past Year Questions (Topic-Wise)

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: