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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Statistics

NTA Abhyas 2020 · Mathematics · Statistics

Two data sets each of size 10 has the variance as 4 and k and the...

Two data sets each of size 1010 has the variance as 44 and kk and the corresponding means as 22 and 44 respectively. If the variance of the combined data set is 5⋅5,5 ⋅ 5, then the value of kk is equal to

Options

  1. A55
  2. B66
  3. C44
  4. D33

Correct answer

A. 55

Step-by-step solution

Combined mean, x−=2×10+4×1020=3\overset{-}{x} = \dfrac{2 \times 10 + 4 \times 10}{20} = 3
d1=x1−−x−=−1{d}_{1} = \overset{-}{{x}_{1}} - \overset{-}{x} = - 1
d2=x2−−x−=1{d}_{2} = \overset{-}{{x}_{2}} - \overset{-}{x} = 1
Combined variance =n1σ12+n2σ2+n1d12+n2d22n1+n2= \dfrac{{n}_{1}{σ}_{1}^{2} + {n}_{2}{σ}^{2} + {n}_{1}{d}_{1}^{2} + {n}_{2}{d}_{2}^{2}}{{n}_{1} + {n}_{2}}
⇒112=10×4+10×k+10×1+10×120⇒ \dfrac{11}{2} = \dfrac{10 \times 4 + 10 \times k + 10 \times 1 + 10 \times 1}{20}
⇒k=5⇒ k = 5
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