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Answers
Answer:
The mean of 10 of them is 15 and the mean of 20 of them is 11.
The last two numbers are 10.
To Find :-
What is the mean of the 32 numbers.
Formula Used :-
\clubsuit♣ Mean Formula :
\begin{gathered}\longmapsto \sf\boxed{\bold{\pink{Mean =\: \dfrac{Sum\: of\: Observations}{Total\: number\: of\: Observations}}}}\\\end{gathered}
⟼
Mean=
TotalnumberofObservations
SumofObservations
Solution :-
First, we have to find the sum of observations of 10 number :
Given :
Mean = 15
Total number of observations = 10
According to the question by using the formula we get,
\implies \sf 15 =\: \dfrac{Sum\: of\: Observations}{10}⟹15=
10
SumofObservations
By doing cross multiplication we get,
\implies \sf Sum\: of\: observations =\: 10(15)⟹Sumofobservations=10(15)
\begin{gathered}\implies \sf Sum\: of\: observations =\: 10 \times 15\\\end{gathered}
⟹Sumofobservations=10×15
\begin{gathered}\implies \sf\bold{\green{Sum\: of\: observations =\: 150}}\\\end{gathered}
⟹Sumofobservations=150
Hence, the sum of observations is 150.
Again, we have to find the sum of observations of 20 number:
Given :
Mean = 11
Total number of observations = 20
According to the question by using the formula we get,
\implies \sf 11 =\: \dfrac{Sum\: of\: Observations}{20}⟹11=
20
SumofObservations
By doing cross multiplication we get,
\implies \sf Sum\: of\: observations =\: 20(11)⟹Sumofobservations=20(11)
\implies \sf Sum\: of\: observations =\: 20 \times 11⟹Sumofobservations=20×11
\implies\sf\bold{\green{Sum\: of\: observations =\: 220}}⟹Sumofobservations=220
Now, we have to find the sum of observations 32 numbers:
\begin{gathered}\implies \sf Sum\: of\: observations =\: 150 + 220 + 10 + 10\\\end{gathered}
⟹Sumofobservations=150+220+10+10
\begin{gathered}\implies \sf Sum\: of\: observations =\: 370 + 20\\\end{gathered}
⟹Sumofobservations=370+20
\implies \sf\bold{\purple{Sum\: of\: observations =\: 390}}⟹Sumofobservations=390
Now, we have to find the mean of the 32 numbers:
Given :
Sum of observations = 390
Total number of observations = 32
According to the question by using the formula we get,
\implies \sf Mean =\: \dfrac{\cancel{390}}{\cancel{32}}⟹Mean=
32
390
\implies \sf Mean =\: \dfrac{\cancel{195}}{\cancel{16}}⟹Mean=
16
195
\implies \sf \bold{\red{Mean =\: 12.1875}}⟹Mean=12.1875
\therefore∴ The mean of the 32 numbers is 12.1875.