Question

how to get the mean in it​

Answer 1

Step-by-step explanation:

$\begin{array}{|c|c|c|c|c|c|} \hline \\ \rm C.I. & \rm c. f . & \rm x_{i} & \rm u_{i}= \dfrac{x_{i}-a }{h}& \rm f_{i} & \rm f_{i} u_{i} \\ \\ \hline 0-10 & 100 & 5 & -3 & 100-90=10 & -30 \\ \hline 10-20 & 90 & 15 & -2 & 90-75=15 & -30 \\ \hline 20-30 & 75 & 25 & -1 & 75-50=25 & -25 \\ \hline 30-40 & 50 & 35 & \rm \red{\boxed{35}}=a &50-25=25 &0 \\ \hline 40-50 & 25 & 45 & 1 & 25-15=10 & 10 \\ \hline 50-60 & 15 & 55 & 2 & 15-5=10 & 20 \\ \hline 60-70 & 5 & 65 & 3 & 5-0=5 & 15 \\ \hline & & & & \rm \Sigma f_{i}=100 & \rm \Sigma f_{i} u_{i} \\ & & & & & =-40 \\ \hline \end{array}$

$\\ \rm\ \[ \therefore \quad \bar{x}=a+h\left[\frac{\sum f_{i} u_{i}}{\sum f_{i}}\right] \]$

[Step deviation method]

$\[ \begin{aligned} \Rightarrow & & \rm \bar{x} &=35+\frac{(-40)(10)}{100} \\ \\ \Rightarrow & && \rm=35-\frac{400}{100}=31 \\ \\ \Rightarrow & & \color{green} \rm\bar{x} &\color{green} \rm=31 \text { years } \end{aligned} \]$

Hence, the mean age of 100 persons =31 years

Answer 2

Answer:

$\color{darkcyan} \underline{ \begin{array}{ || |l| || } \hline \color{magenta} \\ \hline \boxed{ \text{ \tt \: Solution:-} } \end{array}}$

Step-by-step explanation:

$\begin{array}{|c|c|c|c|c|c|} \hline \\ \rm C.I. & \rm c f . & \rm x_{i} & \rm u_{i}= \dfrac{x_{i}-a }{h}& \rm f_{i} & \rm f_{i} u_{i} \\ \\ \hline 0-10 & 100 & 5 & -3 & 100-90=10 & -30 \\ \hline 10-20 & 90 & 15 & -2 & 90-75=15 & -30 \\ \hline 20-30 & 75 & 25 & -1 & 75-50=25 & -25 \\ \hline 30-40 & 50 & 35 & \rm \red{\boxed{35}}=a &50-25=25 &0 \\ \hline 40-50 & 25 & 45 & 1 & 25-15=10 & 10 \\ \hline 50-60 & 15 & 55 & 2 & 15-5=10 & 20 \\ \hline 60-70 & 5 & 65 & 3 & 5-0=5 & 15 \\ \hline & & & & \rm \Sigma f_{i}=100 & \rm \Sigma f_{i} u_{i} \\ & & & & & =-40 \\ \hline \end{array}$

$\\ \rm\ \[ \therefore \quad \bar{x}=a+h\left[\frac{\sum f_{i} u_{i}}{\sum f_{i}}\right] \]$

[Step deviation method]

$\[ \begin{aligned} \Rightarrow & & \rm \bar{x} &=35+\frac{(-40)(10)}{100} \\ \\ \Rightarrow & && \rm=35-\frac{400}{100}=31 \\ \\ \Rightarrow & & \color{green} \rm\bar{x} &\color{green} \rm=31 \text { years } \end{aligned} \]$

Hence, the mean age of 100 persons =31 years