Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Main 20205 SeptemberEvening Shift

Exam: JEE Main
Year: 2020
Date: 5 September
Shift: Evening Shift
Subject: Mathematics
Chapter: Statistics

JEE Main 2020 · 5 September · Evening Shift · Mathematics · Statistics

If the mean and the standard deviation of the data 3, 5, 7, a, b...

If the mean and the standard deviation of the data

3, 5, 7, a, b

are

5

and

2

respectively, then

a

and

b

are the roots of the equation:

Options

A ${x}^{2} - 10x + 18 = 0$
B $2{x}^{2} - 20x + 19 = 0$
C ${x}^{2} - 10x + 19 = 0$
D ${x}^{2} - 20x + 18 = 0$

Correct answer

C. ${x}^{2} - 10x + 19 = 0$

Step-by-step solution

5 + 3 + 7 + a + b = 25 ⇒ a + b = 10

S.D.

= \sqrt{\dfrac{{5}^{2} + {3}^{2} + {7}^{2} + {a}^{2} + {b}^{2}}{5} - {5}^{2}} = 2

= \dfrac{{a}^{2} + {b}^{2} + 83}{5} - 25 = 4 ⇒ {a}^{2} + {b}^{2} = 62

⇒ ( a + b{)}^{2} - 2ab = 62 ⇒ ab = 19

so equation whose roots are a and b is

{x}^{2} - 10x + 19 = 0

Practice Statistics on Quantrex Academy →

More from Statistics

Consider a data consisting of 10 observations x_1, x_2, …, x_ 10 , whose mean is 5 and… JEE Advanced 2026 A set of four observations has mean 1 and variance 13 . Another set of six observations… JEE Main 2026 Let the mean and the variance of seven observations 2, 4, α, 8, β, 12, 14 , α < β , be 8… JEE Main 2026 A data consists of 20 observations x_1, x_2, …, x_ 20 . If ∑_ i=1 ^ 20 (x_i + 5)^2 = 2500… JEE Main 2026 A variable X takes values 0, 0, 2, 6, 12, 20, …, n(n-1) with frequencies ^nC_0, ^nC_1… JEE Main 2026 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… JEE Main 2026 For 10 observations x_1, x_2, …, x_ 10 , if ∑_ i=1 ^ 10 (x_i+2)^2=180 and ∑_ i=1 ^ 10… JEE Main 2026 Suppose that the mean and median of the non-negative numbers 21, 8, 17, a, 51, 103, b… JEE Main 2026 The mean and variance of n observations are 8 and 16 , respectively. If the sum of the… JEE Main 2026 If 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… JEE Main 2026 The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these… JEE Main 2026 Let X=\ x ∈ ~N: 1 ≤ x ≤ 19\ and for some a, b ∈ ℝ, Y=\ a x+b: x ∈ X\ . If the mean and… JEE Main 2026 The mean and variance of a data of 10 observations are 10 and 2, respectively. If an… JEE Main 2026 If the mean and the variance of the data Class 4-8 8-12 12-16 16-20 Frequency 3 λ 4 7 are… JEE Main 2026 Let the mean and variance of 8 numbers -10,-7,-1, x, y, 9,2,16 be (7)/(2) and (293)/(4)… JEE Main 2026 If the mean deviation about the median of the numbers k, 2 k, 3 k, …. ., 1000 k is 500… JEE Main 2026 Full Statistics list Statistics JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs