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

The means of two samples of size 40 and 50 were found to be 54 and...

The means of two samples of size 4040 and 5050 were found to be 5454 and 6363 respectively. Their standard deviations were 66 and 99 respectively. The variance of the combined sample of size 9090 is

Options

  1. A9090
  2. B77
  3. C99
  4. D8181

Correct answer

D. 8181

Step-by-step solution

n1=40{n}_{1} = 40, n2=50{n}_{2} = 50
x¯1=54{\overset{¯}{x}}_{1} = 54, x¯2=63{\overset{¯}{x}}_{2} = 63
σ1=6{\sigma}_{1} = 6, σ2=9{\sigma}_{2} = 9
x¯=n1x¯1+n2x¯2n1+n2=40×54+50×6390=59\overset{¯}{x} = \dfrac{{n}_{1}{\overset{¯}{x}}_{1} + {n}_{2}{\overset{¯}{x}}_{2}}{{n}_{1} + {n}_{2}} = \dfrac{40 \times 54 + 50 \times 63}{90} = 59
d1=x¯−x¯1=5{d}_{1} = \overset{¯}{x} - {\overset{¯}{x}}_{1} = 5
d2=x¯2−x¯=4{d}_{2} = {\overset{¯}{x}}_{2} - \overset{¯}{x} = 4
Combined S.D=n1d12+n2d22+n1σ12+n2σ22n1+n2S. D = \sqrt{\dfrac{{n}_{1}{d}_{1}^{2} + {n}_{2}{d}_{2}^{2} + {n}_{1}{\sigma}_{1}^{2} + {n}_{2}{\sigma}_{2}^{2}}{{n}_{1} + {n}_{2}}}
=40×25+50×16+40×36+50×8190= \sqrt{\dfrac{40 \times 25 + 50 \times 16 + 40 \times 36 + 50 \times 81}{90}}
=9= 9
Variance =81= 81
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