Question

Consider the following hypothetical hourly wages for a group college students:

14.00 15.79 14.97 15.18 14.53 16.28 15.31 13.04

15.63 14.37 14.75 15.58 15.25 16.81 13.86 15.93

16.87 14.91 14.20 13.53 15.40 15.45 15.87 16.22

a. Construct a histogram on a separate page for the above data. Make sure to label and scale x and y-axes.

b. Describe the shape of the distribution

c. Hypothesize how the mean and the median compare, considering the shape of the distribution.

d. Compute the mean and the median.

e. If you were discussing what is the typical wages that college students is earning, would it matter which measure you would report?

Next consider the following hypothetical hourly wages for a group of students from a competing school, like the city college

14.56 16.68 15.15 15.38 13.56 16.42 14.26 14.77

15.62 13.83 48.28 14.55 15.39 15.51 13.79 13.92

43.50 16.92 15.90 14.61 13.63 14.75 15.37 16.03

13.92

f. Construct a histogram. Make sure to label and scale x and y-axes.

g. Describe the shape of the distribution

h. Hypothesize how the mean and the median compare, considering the shape of the distribution.

i. Compute the mean and the median.

J. What measure should be reported to a student who is prospecting a parttime job and what kind of wages should they expect?

Conclusion:

In a symmetrical distribution ____________ in a skewed distribution__________

Answer 1

a)  

b) Shape of the histogram is symmetrical bell shaped     
This histogram shows a Normal distribution curve     
      
c) Since, the shape of the distribution is a bell cuve that is the distribution     
is apparently a normal distribution, the mean and the median of the      
distribution are approximately the same.     
      
d) Compute mean using Excel function average     
Compute median using Excel function median     
Mean = 15.16     
Median = 15.28    
      
e) Since Mean and Median are approximately the same, we can report      
any of the two measures for discussing the typical wages of the college students     
earning     

f)

g) Shape of the distribution is a skewed distribution.
This is a positively or right skewed distribution
  
h) For a Positively skewed distribution, the Mean is larger than the Median
  
i) Compute mean using Excel function average
Compute median using Excel function median
Mean = 17.452
Median = 15.15
  
j) Since it is a skewed distribution, we should report the Median
to the student prospecting a part time job
Thus the student should expect a wage of $15.15
  
  
Conclusion :
In a symmetrical distribution Mean and Median are the same
In a skewed distribution Mean is larger than the Median.