Question

Mean of a set of 8 observations is 10 and 4
is the mean of a set of 7 observations. The
mean of the combined set is given by:
(a) 10.8
(b) 7.2
(c) 8.2
(d) 12​

Answer 1

Answer:

$\huge\star \underline{ \boxed{ \purple{Answer}}}\star$

$\sf\green{The\:correct\:answer\:is\:option\:B\:7.2}$

Step-by-step explanation:

Given :-

Mean of a set of 8 observations is 10

4 is the mean of a set of 7 observations

To Find :-

The

Themean of the combined set is given by:

Solution :-

$\sf{let\:the\:1^st\:mean\:be\:x_1}$

$\sf{let\:the\:2^nd\:mean\:be\:x_2}$

&

$\sf{let\:the\:1^st\:no.\:of\:observations\:be\:w_1}$

$\sf{let\:the\:2^nd\:no\:of\:observations\:be\:w_2}$

➝$\sf{x\:=\:\frac{x_1 w_1\:+\:x_2 w_2}{w_1\:+\:w_2}}$

➝$\sf{\frac{10\:\times\:8\:+\:7\:\times\:4}{7\:+\:3}}$

➝$\sf{\frac{80\:+\:28}{8\:+\:7}}$

➝$\sf{\cancel\frac{108}{15}\:7.2}$

➝$\sf{7.2}$

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