Math, asked by ajj17224, 24 days ago

the mean of 20 observations is 18 and the mean of other 30 observations is 22. Find the mean of all these 50 observations​

Answers

Answered by BrainlyTwinklingstar
12

Given :

Total number of observations : 50

Mean of 20 observations : 18

Mean of 30 observations : 22

To find :

The mean of all those observations.

Solution :

We know that, the means of 20 and 30 observations seperataly are 18 and 22 respectively. So, first we should find the sum of observations that we get while finding the mean seperataly.

Sum of 20 observations :

\sf \dashrightarrow Mean = \dfrac{Sum \: of \: observations}{Number \: of \: observations}

\sf \dashrightarrow 18 = \dfrac{Sum \: of \: observations}{20}

\sf \dashrightarrow Sum \: of \: observations = 20 \times 18

\sf \dashrightarrow Sum \: of \: observations = 360

Sum of 30 observations :

\sf \dashrightarrow Mean = \dfrac{Sum \: of \: observations}{Number \: of \: observations}

\sf \dashrightarrow 22 = \dfrac{Sum \: of \: observations}{30}

\sf \dashrightarrow Sum \: of \: observations = 22 \times 30

\sf \dashrightarrow Sum \: of \: observations = 660

Now, we can find the mean of all the observations together.

Mean of all observations :

\sf \dashrightarrow Mean = \dfrac{Sum \: of \: observations}{Number \: of \: observations}

\sf \dashrightarrow Mean = \dfrac{360 + 660}{50}

\sf \dashrightarrow Mean = \dfrac{1020}{50}

\sf \dashrightarrow Mean = 20.4

Hence, the mean of all the observations is 20.4.

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