Exercise 2.4. (DO NOT EAT WHILE WORKING ON A COMPUTER) At a university, Amy took

Question

Exercise 2.4. (DO NOT EAT WHILE WORKING ON A COMPUTER) At a university, Amy took a random sample of 200+DGC-.AMS faculty members.. Amy estimated that the average salary of a faculty member is $65,000 with a standard deviation of $10,000. The medi salary is $67,000 and one senior faculty has a maximum salary of $80,000. an (I) Amy claims that the distribution of salaries on the campus is skewed to the left. Do you agree with her? Justify her claim and state her assumptions. Amy eating and working Ges, the diadnbution of the Salanes onthe compusis hesed to the lett because the mean

Explanation / Answer

I)

Yes the distribution is left skew because in a left skew distribution mean<median<mode

given mean=65000

median= 67000

as mean< median it is left skew

II)

Largest value got changed from 80,000 to 800,000

a) The median salary remains the same at 67000

b) The mean is calculated by adding all the numbers and dividing it by the total number of points

Here the value has changed from 80,000 to 800,000

the difference divided by the total number of data points =(800,000 -80,000)=720000

72000/245=2938.776=2939 ( rounded)

Hence the mean value will increase from 65000 to 65000+2939=67939

c) 67939(mean)>67000 (median)

hence right skew distribution

e)

Coefficient of Variation is calculated as

(Standard deviation/ Mean)*100

=(10000/65000)*100=15.385 before the change

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