Here are the summary statistics for the weekdy payroll of a small company lowest

Question

Here are the summary statistics for the weekdy payroll of a small company lowest salary-$250, mean salary-$600, median-$900, range-S1400, laR-S800, first quartile·$450, standard deviation-S300 a) Do you think the distribution of salaries is symmetric, skewed to the left, or skewed to the right? Explain why O A. The distribution is symmetrio because the mean is less than the median. OB· The distrbution is skewed to the right because the mean is less han the median. OC. The distribution is skewed to the loft because the mean is less than the median. 0 D. There is not enough information to estimate the shape of the distribution. b) Between what two values ao the middle 50% of the salaries found? The midde 50% of te salaries aro found between and S c) Suppose business has been good and the oompany gives each employee a $50 raise. Tell the new value of each of the summary statistics Ater everyone receives a $50 raise, the new lowest salary is s Ater everyone receives a $50 raise, the new mean salary is Afher everyone receives a $50 raise, the new median is s After everyone receives a $50 raise, the new range is Aher overyone receives a S50 raisethe new IQR iss» Aher overyone receves a S50 raise, te new frst quartie is S Aner overyone receives a SSO raise, the new standard deviaton is

Explanation / Answer

a) C. The distribution is skewed to the left because the mean is less than the median

b) The middle 50% is between first quartile and third quartile

First quartile = $450

Third quartile = first quartile + IQR = 450 + 800 = $1250

The middle 50% of salaries are found between $450 and $1250

c) The lowest new salary = $300

The new mean salary = $650

The new median = $950

The new range = $1400

The new IQR = $800

The new first quartile = $500

The new standard deviation = $300

d) The new lowest salary = 250x1.2 = $300

The new mean salary = 600x1.2 = $720

The new median = 900x1.2 = $1080

The new range = 1400x1.2 = $1680

The new IQR = 800x1.2 = $960

The new first quartile = 450x1.2 = $540

The new standard deviation = 300x1.2 = $360

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