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Q.

.       Consider the statistics of two sets of observations as follows:                                      Size                      Mean                       Variance           Observation I       10                         2                           2          Observation II       n                          3                           1          If the variance of the combined set of these two observations is 179, then the value of n is equal to:

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answer is 5.

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Detailed Solution

For group -1:∑xi10=2⇒∑xi=20 ∑xi210-(2)2=2⇒∑xi2=60 For group -2:∑yin=3⇒∑yi=3n∑yi2n-32=1⇒∑yi2=10n.   Now, combined variance σ2=∑xi2+yi210+n-∑xi+yi10+n2⇒179=60+10n10+n-(20+3n)2(10+n)2⇒17n2+20n+100=9n2+40n+200⇒8n2-20n-100=0⇒2n2-5n-25=0⇒n=5
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