JEE Main 2026 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 6 April 2026, Shift 1, Maths Q9

Question 9 of 75 in this shift, Maths question 9 of 25, Section A.

A 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 the ratio of mean to standard deviation of this data is:

(1)2:1
(2)3:1Official answer
(3)3:2
(4)4:1

Official answer

Option 2

NTA final key.

Chapter: Statistics
Topic: Variance and SD
Idea tested: Algebraic Expansion of Squared Deviations

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 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
2 Apr 2025, Shift 2 · Q8If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then $a+b+ab$ is equal to :MediumSingle 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. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.