If the mean of the frequency distribution | Class : | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | | Frequency : | 2 | 3 | $x$ | 5 | 4 | is 28, then its variance is ____________.

JEE Main 2023 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 10 April 2023, Shift 1, Maths Q30

Question 30 of 90 in this shift, Maths question 30 of 30, Section B.

If the mean of the frequency distribution

Class :	0-10	10-20	20-30	30-40	40-50
Frequency :	2	3	$x$	5	4

is 28, then its variance is ____________.

The figure, in words

Frequency table: classes 0-10, 10-20, 20-30, 30-40, 40-50 with frequencies 2, 3, x, 5, 4.

Official answer

151

NTA final key.

Chapter: Statistics
Topic: Variance and SD
Idea tested: Variance of Continuous Grouped Data

Same topic in other shifts

All Variance and SD questions

2 Apr 2026, Shift 1 · Q8If the mean of the data | Class | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | | Frequency | 2 | $k$ | 28 | 54 | $k+1$ | 5 | is $21$ ,…MediumSingle correct
2 Apr 2026, Shift 2 · Q9The mean and variance of $n$ observations are 8 and 16, respectively. If the sum of the first $(n - 1)$ observations is 48 and the sum of…EasySingle correct
4 Apr 2026, Shift 2 · Q8For 10 observations $x_1,x_2,\ldots,x_{10}$ , if $\sum_{i=1}^{10}(x_i+2)^2=180$ and $\sum_{i=1}^{10}(x_i-1)^2=90$ , then their standard…MediumSingle correct
6 Apr 2026, Shift 1 · Q9A data consists of 20 observations $x_1, x_2,\ldots, x_{20}$ . If $\sum_{i=1}^{20}(x_i+5)^2=2500$ and $\sum_{i=1}^{20}(x_i-5)^2=100$ , then…MediumSingle correct
6 Apr 2026, Shift 2 · Q8Let the mean and the variance of seven observations $2, 4, \alpha, 8, \beta, 12, 14$ , $\alpha<\beta$ , be 8 and 16 respectively. Then the…MediumSingle correct
8 Apr 2026, Shift 2 · Q7A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of…EasySingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. This question needs a figure we do not reproduce; it is described in words above. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.