Question

7. a) The mean and standard deviation of the salaries of the two factories are provided below: Factory No. of Employees Mean Salary SD of Salary А 30 Rs.4800 Rs.10 B 20 Rs.5000 Rs. 12 Find the combined mean salary and standard deviation of salary. 11) Examine which factory has more consistent structure so far as satisfying its employees are concerned. ​

Answer 1

"It seems this what you are looking for"

The mean and standard deviation of the salaries of the two factories are provided below:

Factory          No. of Employees      Mean Salary         SD of Salary

A                       30                             Rs.4800                   Rs.10

B                       20                             Rs.5000                    Rs.12  

(1) Find the combined mean salary and standard deviation of salary.

(2) Examine which factory has more consistent structure so far as satisfying its employees are concerned. ​

Answer:

The combined mean salary is equal to 6400 and combined standard deviation of salary is equal to 98.57.

Step-by-step explanation:

Given: n₁ = 30 and n₂ = 20

$\bar{X_1}=4800$  and $\bar{X_2}=5000$

σ₁ = 10 and σ₂ = 12

Here, n₁  is the number of employees in factory A and $\bar{X_1}$ is its mean salary  and  n₂  is the number of employees  in factory B and $\bar {X_2}$ is its mean salary.

Combined mean salary ($\bar{X}$) is given by:

$\bar{X} =\frac{n_1\bar{X_1}+{n_2\bar{X_2}}}{n_1+n_2}$

$\bar{X} =\frac{(30)(4800)+(20)(5000)}{30+20}$

$\bar{X}=\frac{244000}{50}$

$\bar{X} =4880$

$d_1^2=(\bar{X_1}-\bar{X}) =(4800-4880)^2=6400$

$d_2^2=(\bar{X_2}-\bar{X}) =(5000-4880)^2=14400$

Combined standard deviation (σ) is given by:

$\sigma = \sqrt{\frac{n_1\sigma_1^2+n_2\sigma_2^2+n_1d_1^2+n_2d_2^2}{n_1 +n_2} }$

$\sigma = \sqrt{\frac{(30)(10)^2+(20)(12)^2+(30)(6400)+(20)(14400)}{50} }$

$\sigma = \sqrt{9717.6}$

$\sigma =98.57$

(ii) consistent structure:

$C.V.(A)=\frac{\sigma _1}{X_1}\times 100= \frac{10}{4800}\times 100=0.208\%$

$C.V.(B)=\frac{\sigma _2}{X_2}\times 100= \frac{20}{5000}\times 100=0.4\%$

Because CV (A) < CV (B)

Therefore, factory A has more consistent structure so far as satisfying its employees are concerned.

To learn more about " Combined or polled mean"

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Answer 2

answer: (i) combined mean = 4880

standard deviation mean =98.57

(ii) cv(A) < cv(B)

hence factory A has more consistent structure so far as satisfying its employed are concerned.