Two data sets each of size 10 has the variance as 4 and k and the corresponding means as 2 and 4 respectively. If the variance of the combined data…

Question

Two data sets each of size 10 has the variance as 4 and k and the corresponding means as 2 and 4 respectively. If the variance of the combined data set is 5⋅5, then the value of k is equal to

MARKS Content Team · Accepted Answer

Correct answer: (A) 5. Combined mean, x-=(2×10+4×10)/20=3 d_1=x_1--x-=-1 d_2=x_2--x-=1 Combined variance =(n_1σ12+n_2σ^2+n_1d12+n_2d22)/(n_1+n_2) ⇒11/2=(10×4+10×k+10×1+10×1)/20 ⇒k=5

Two data sets each of size $10$ has the variance as $4$ and $k$ and the corresponding means as $2$ and $4$ respectively. If the variance of the combined data set is $5 \cdot 5,$ then the value of $k$ is equal to

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