The mean of 16 numbers is 48. If each number is divided by 4 and diminished by 3, then the new mean is
Answers
Answer:
hu
let \: the \: numbers \: be \: x_{1} \: x_{2} \: x_{3} ..... x_{12}.letthenumbersbex
1
x
2
x
3
.....x
12
.
Total number = 12
Mean = 40
\begin{lgathered}\frac{sum \: of \: all \: observation}{total \: number \: of \: observation} = 40 \\ \\ \frac{x_{1} + x_{2} + x_{3} + .... + x_{12}}{12} = 40 \\ \\ x_{1} + x_{2} + x_{3} + .... + x_{12} = 40 \times 12 \\ \\ x_{1} + x_{2} + x_{3} + .... + x_{12} = 480\end{lgathered}
totalnumberofobservation
sumofallobservation
=40
12
x
1
+x
2
+x
3
+....+x
12
=40
x
1
+x
2
+x
3
+....+x
12
=40×12
x
1
+x
2
+x
3
+....+x
12
=480
Each number is divided by 8.
\begin{lgathered}new \: mean = \frac{new \: total \: marks}{new \:number \: of \: terms } \\ \\new \: mean = \frac{ \frac{x_{1} + x_{2} + x_{3} + .... + x_{12}}{8} }{12} \\ \\ new \: mean \: = \frac{x_{1} + x_{2} + x_{3} + .... + x_{12}}{12 \times 8} \\ \\ new \: mean = \frac{480}{96} \\ \\ new \: mean = 5\end{lgathered}
newmean=
newnumberofterms
newtotalmarks
newmean=
12
8
x
1
+x
2
+x
3
+....+x
12
newmean=
12×8
x
1
+x
2
+x
3
+....+x
12
newmean=
96
480
newmean=5
So, the new mean is 5 of the number after dividing them by 8 .