. 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:

Question

.       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:

Infinity Learn · Accepted Answer

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 σ$$2=$$∑$$xi2+yi210+n-$$∑$$xi+yi10+n2$$⇒$$179=60+10n10+n-(20+3n)2(10+n)2$$⇒$$17n2+20n+100=9n2+40n+200$$⇒$$8n2-20n-100=0$$⇒$$2n2-5n-25=0$$⇒$$n=5$$

. 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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