LIR 832:
Problem Set #1
Calculating Means, Variances and Standard Deviations:
1.
Absenteeism in our plant varies considerably from day to day.
Over the last ten days the
number of employees absent has been
10, 15, 5, 6, 7, 22, 3, 14, 8, 21
a.
Calculate the mean, variance and standard deviation of absences. The plant has 80
employees.
Repeat these calculations for the percent of employees absent.
b.
Calculate the median and mode for this data set for the values.
How do the
median, mode and mean compare?
2.
The midterm test for a statistics course has a time limit of 1 hour.
However, like most
statistics exams, this one was quite easy.
To assess how easy, the professor recorded the
amount of time taken by a sample of nine students to hand in their test papers.
The times,
rounded to the nearest minute, are
33
29
45
60 42
19
52
38
36
a.
compute the mean, median and mode.
What can you learn about the exam from
these three statistics?
3.
A plant which is under our supervision is in the midst of an organizing drive by Local 9 of
the United Clerical Employees.
There are ten employees in the clerical unit at this plant.
Prior
subtle and illegal research suggests that 45% of our clerical employees at all of our locations,
sympathic to union representation.
Using the binomial distribution, what is the likelihood that
six or more of the employees in this ten employee unit will vote for a union?
To calculate this
outcome, you will need to use the binomial formula and calculate the likelihood of six, seven,
eight, nine or ten employees will vote for a union (and then add these probabilities).
Before
trying to use the formula you will need to establish:
a.
What is the probability of a success (a vote for the union)?
b.
What is the probability of a failure (a vote against the union)?
c.
What is the total number of experiments?
d.
What is the number of successes (this will vary with the outcome you are
calculating).
Remember, n! is n*(n-1)*(n-2)*(n-3)*.
....5*4*3*2*1 and 0! = 1
so, for example, 6! = 6*5*4*3*2*1.