Mathematics: There are 39 employees in a particular division of a company. their salaries have a mean of $70,000, a median of $55,000, and a standard deviation of $20,000. the largest number on the list is $100,000. by accident, this number is changed to $1,000,000. a)what is the value of the mean after the change? write your answer in units of $1000.b)what is the value of the median after the change? write your answer in units of $1000.c)what is the value of the standard deviation after the change? write your

17,13,11Step-by-step explanation:...

There are 39 employees in a particular division

Ответ:

silvernekoo

11.01.2022

Mathematics

a) New mean 78.07692308 thousands of dollars

b) The median does not vary

c) New standard deviation 150.1793799 thousands of dollars

Step-by-step explanation:

We are working in units of $1,000

a)What is the value of the mean after the change?

Let

s_1,s-2,...,s_38

be the salaries of the employees that earn less than 100 units.

The mean of the 39 salaries is 55 units so

$\displaystyle\frac{s_1+s_2+...+s_{38}+100}{39}=55$

and

$s_1+s_2+...+s_{38}+100=55*39=2145$

By accident, the 100 on the left is changed to 1,000

$s_1+s_2+...+s_{38}+100+900=55*39=2145+900\Rightarrow \\\\\Rightarrow s_1+s_2+...+s_{38}+1000=3045$

Dividing by 39 both sides, we get the new mean

$\displaystyle\frac{s_1+s_2+...+s_{38}+1000}{39}=\displaystyle\frac{3045}{39}=78.07692308$

b)What is the value of the median after the change?

Since the number of data does not change and only the right end of the range of salaries is changed, the median remains the same; 55

c)What is the value of the standard deviation after the change?

The variance is 400, so

$\displaystyle\frac{(s_1-70)^2+(s_2-70)^2+...+(s_{38}-70)^2+(100-70)^2}{39}=400\Rightarrow\\\\\Rightarrow (s_1-70)^2+(s_2-70)^2+...+(s_{38}-70)^2+(100-70)^2=400*39=15600$

Adding 864,000 to both sides we get

$(s_1-70)^2+(s_2-70)^2+...+(s_{38}-70)^2+(100-70)^2+864000=15600+864000\Rightarrow\\\\\Rightarrow (s_1-70)^2+(s_2-70)^2+...+(s_{38}-70)^2+(1000-70)^2=879600$

Dividing by 39 and taking the square root we get the new standard deviation

$\displaystyle\frac{(s_1-70)^2+(s_2-70)^2+...+(s_{38}-70)^2+(1000-70)^2}{39}=\displaystyle\frac{879600}{39}=22553.84615\Rightarrow\\\\\Rightarrow \sqrt{\displaystyle\frac{(s_1-70)^2+(s_2-70)^2+...+(s_{38}-70)^2+(1000-70)^2}{39}}=150.1793799$

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