Respuesta :
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
[tex]\frac{\sum X}{n}[/tex] = $70,000 ⇒ [tex]\sum X[/tex] = 70,000 * 10 = $700,000
New [tex]\sum X[/tex] after change = $700,000 - $100,000 + $1,000,000 = $1600000
Therefore, New mean = [tex]\frac{1600000}{10}[/tex] = $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 = [tex]20000^{2}[/tex] i.e. [tex]20000^{2}[/tex] = [tex]\frac{\sum x^{2} - n*xbar }{n -1}[/tex]
Original [tex]\sum x^{2}[/tex] = ([tex]20000^{2}[/tex] * (10-1)) + (10 * 70,000) = $3,600,700,000
New [tex]\sum x^{2}[/tex] = $3,600,700,000 - [tex]100,000^{2} + 1,000,000^{2}[/tex] = 9.936007 * [tex]10^{11}[/tex]
New Variance = [tex]\frac{new\sum x^{2} - n*new xbar }{n -1}[/tex] = [tex]\frac{9.936007 *10^{11} - 10*160000 }{10 -1}[/tex] = 1.103999 * [tex]10^{11}[/tex] Therefore, standard deviation after change = [tex]\sqrt{1.103999 * 10^{11} }[/tex] = $332264.804 .
