Question

A small warehouse employs a supervisor at $1200 a week, an inventory manager at $700 a week, six stock boys at $400 a week, and four drivers at $500 a week.

a) Find the mean and median wage.

b) How many employees earn more than the mean wage?

c) Which measure of center best describes a typical wage at this company: the mean or the median?

d) Which measure of spread would best describe the payroll: the range, the IQR, or the standard deviation?

e) Is the distribution symmetric or skewed? Explain.

Typed answers please

Answer 1

Xi	Fi	Xi*Fi	Xi*Fi^2	C. Fi
1200	1	1200	1200	1
700	1	700	700	2
400	6	2400	14400	8
500	4	2000	8000	12
sum	12	6300	24300

a)              
mean = sum(Xi*Fi)/Sum(Fi)              
525              
              
median = average of (n/2)th and (n/2 + 1)th observation              
average of 6th and 7th observation              
400              
              
b)              
Number of employyes more than 525 is 4              
              
c)              
from the histogram I can say that the distribution is negatively skewed              
hence, median is the best measure of central tendency              
              
d)              
for a skewed distribution, IQR is the best measure of dispersion              
              
e)

from the histogram I can say that the distribution is negatively skewed              

Histogram 1200 700 400 500