Question

There are 10 employees in a particular division of a company. Their salaries have a mean of 570,000, a median of $55,000,and a standard deviation of 520,000. 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?b. What is the value of the median after the change?c. What is the value of the standard deviation after the change?

Answer 1

Answer:

a) $160,000

b) $55,000

c) $332264.804

Step-by-step explanation:

We are given that there are 10 employees in a particular division of a company and their salaries have a mean of $70,000, a median of $55,000, and a standard deviation of $20,000.

And also the largest number on the list is $100,000 but By accident, this number is changed to $1,000,000.

a) Value of mean after the change in value is given by;

     Original Mean = $70,000

       $\frac{\sum X}{n}$ = $70,000  ⇒ $\sum X$ = 70,000 * 10 = $700,000

   New $\sum X$ after change = $700,000 - $100,000 + $1,000,000 = $1600000

  Therefore, New mean = $\frac{1600000}{10}$ = $160,000 .

b) Median will not get affected as median is the middle most value in the data set and since $1,000,000 is considered to be an outlier so median remain unchanged at $55,000 .

c) Original Variance = $20000^{2}$ i.e.  $20000^{2}$ = $\frac{\sum x^{2} - n*xbar }{n -1}$

    Original $\sum x^{2}$ = ($20000^{2}$ * (10-1)) + (10 * 70,000) = $3,600,700,000

    New $\sum x^{2}$ = $3,600,700,000 - $100,000^{2} + 1,000,000^{2}$ = 9.936007 * $10^{11}$  

    New Variance = $\frac{new\sum x^{2} - n*new xbar }{n -1}$ = $\frac{9.936007 *10^{11} - 10*160000 }{10 -1}$ = 1.103999 * $10^{11}$    Therefore, standard deviation after change = $\sqrt{1.103999 * 10^{11} }$ = $332264.804 .