Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Statistics

NTA Abhyas 2020 · Mathematics · Statistics

If ∑ _ i = 1 ^ 5 ( x _ i - 6) = 5 and ∑ _ i = 1 ^ 5 ( x _ i - 6) ^...

If ∑i=15(xi−6)=5\mathop{∑}_{i = 1}^{5}\left({x}_{i} - 6\right) = 5 and ∑i=15(xi−6)2=25\mathop{∑}_{i = 1}^{5}{\left({x}_{i} - 6\right)}^{2} = 25, then the standard deviation of observations 3x1+2,3x2+2,3x3+2,3{x}_{1} + 2,3{x}_{2} + 2,3{x}_{3} + 2,3x4+23{x}_{4} + 2 and 3x5+23{x}_{5} + 2 is equal to

Correct answer

6

Step-by-step solution

Variance of (3xi+2)=9var(xi)\left(3{x}_{i} + 2\right) = 9var ( {x}_{i} )
=9(∑xi25−(∑xi5)2)= 9\left(\dfrac{∑ {{x}_{i}}^{2}}{5} - {\left(\dfrac{∑ {x}_{i}}{5}\right)}^{2}\right)
=9(5−1)= 9\left(5 - 1\right)
=36= 36
⇒S.D=6⇒ S . D = 6
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 2026A set of four observations has mean 1 and variance 13 . Another set of six observations… JEE Main 2026Let the mean and the variance of seven observations 2, 4, α, 8, β, 12, 14 , α < β , be 8… JEE Main 2026A data consists of 20 observations x_1, x_2, …, x_ 20 . If ∑_ i=1 ^ 20 (x_i + 5)^2 = 2500… JEE Main 2026A variable X takes values 0, 0, 2, 6, 12, 20, …, n(n-1) with frequencies ^nC_0, ^nC_1… JEE Main 2026The 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 2026For 10 observations x_1, x_2, …, x_ 10 , if ∑_ i=1 ^ 10 (x_i+2)^2=180 and ∑_ i=1 ^ 10… JEE Main 2026Suppose that the mean and median of the non-negative numbers 21, 8, 17, a, 51, 103, b… JEE Main 2026The mean and variance of n observations are 8 and 16 , respectively. If the sum of the… JEE Main 2026If 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 2026The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these… JEE Main 2026Let X=\ x ∈ ~N: 1 ≤ x ≤ 19\ and for some a, b ∈ ℝ, Y=\ a x+b: x ∈ X\ . If the mean and… JEE Main 2026The mean and variance of a data of 10 observations are 10 and 2, respectively. If an… JEE Main 2026If 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 2026Let the mean and variance of 8 numbers -10,-7,-1, x, y, 9,2,16 be (7)/(2) and (293)/(4)… JEE Main 2026If 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 PYQsJEE Mathematics PYQs All NTA Abhyas JEE Main PYQs