The mean deviation about the mean for the data x_i 5 7 9 10 12 15 f_i 8 6 2 2 2 6 is equal to:

Correct answer: C. (44)/(13) Mean x = (∑ f_i x_i)/(∑ f_i) ∑ f_i = 8 + 6 + 2 + 2 + 2 + 6 = 26 ∑ f_i x_i = 8(5) + 6(7) + 2(9) + 2(10) + 2(12) + 6(15) ∑ f_i x_i = 40 + 42 + 18 + 20 + 24 + 90 = 234 x = (234)/(26) = 9 Mean deviation about mean = ∑ f_i |x_i - x | ∑ f_i ∑ f_i |x_i - x | = 8|5 - 9| + 6|7 - 9| + 2|9 - 9| + 2|10 - 9| + 2|12 - 9| + 6|15 - 9| ∑ f_i |x_i - x | = 8(4) + 6(2) + 2(0) + 2(1) + 2(3) + 6(6) ∑ f_i |x_i - x | = 32 + 12 + 0 + 2 + 6 + 36 = 88 Mean deviation = (88)/(26) = (44)/(13) Answer: (44)/(13)

JEE Main 20265 AprilMorning Shift

Exam: JEE Main
Year: 2026
Date: 5 April
Shift: Morning Shift
Subject: Mathematics
Chapter: Statistics

JEE Main 2026 · 5 April · Morning Shift · Mathematics · Statistics

The mean deviation about the mean for the data x_i 5 7 9 10 12 15...

The mean deviation about the mean for the data

$x_i$	$5$	$7$	$9$	$10$	$12$	$15$
$f_i$	$8$	$6$	$2$	$2$	$2$	$6$

is equal to:

Options

A $\dfrac{40}{13}$
B $\dfrac{42}{13}$
C $\dfrac{44}{13}$
D $\dfrac{46}{13}$

Correct answer

C. $\dfrac{44}{13}$

Step-by-step solution

Mean

\bar{x} = \dfrac{\sum f_i x_i}{\sum f_i}

\sum f_i = 8 + 6 + 2 + 2 + 2 + 6 = 26

\sum f_i x_i = 8(5) + 6(7) + 2(9) + 2(10) + 2(12) + 6(15)

\sum f_i x_i = 40 + 42 + 18 + 20 + 24 + 90 = 234

\bar{x} = \dfrac{234}{26} = 9

Mean deviation about mean

= \dfrac{\sum f_i |x_i - \bar{x}|}{\sum f_i}

\sum f_i |x_i - \bar{x}| = 8|5 - 9| + 6|7 - 9| + 2|9 - 9| + 2|10 - 9| + 2|12 - 9| + 6|15 - 9|

\sum f_i |x_i - \bar{x}| = 8(4) + 6(2) + 2(0) + 2(1) + 2(3) + 6(6)

\sum f_i |x_i - \bar{x}| = 32 + 12 + 0 + 2 + 6 + 36 = 88

Mean deviation

= \dfrac{88}{26} = \dfrac{44}{13}

Answer:

\dfrac{44}{13}

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