JEE Advanced 2023 Paper 1 · Q15 · Mean/Median/Mode

Question

Consider the given data with frequency distribution: $x_i: 3, 8, 11, 10, 5, 4$ with frequencies $f_i: 5, 2, 3, 2, 4, 4$. Match each entry in List-I to the correct entries in List-II.
List-I:
(P) The mean of the above data is
(Q) The median of the above data is
(R) The mean deviation about the mean of the above data is
(S) The mean deviation about the median of the above data is
List-II: (1) $2.5$, (2) $5$, (3) $6$, (4) $2.7$, (5) $2.4$

SolveKar AI · Accepted Answer

Sort data: $x_i = 3,4,5,8,10,11$ with $f_i = 5,4,4,2,2,3$, total $\sum f_i = 20$. $\sum f_i x_i = 15 + 16 + 20 + 16 + 20 + 33 = 120$. Mean $= 120/20 = 6$ — (3). Cumulative freq at $5$ reaches $13 \ge 10$, so median is the $10$th observation $= 5$ — (2). Mean deviation about mean: $\sum f_i |x_i - 6| / 20 = 54/20 = 2.7$ — (4). Mean deviation about median: $\sum f_i |x_i - 5| / 20 = 48/20 = 2.4$ — (5).

JEE Advanced 2023 Paper 1 · Q15 · Mean/Median/Mode

Solution