Help on Frequency Distribution - disagreement with professor

[Tami]

Help on "Frequency Distribution" - disagreement with professor...

Homework Statement

Refer to the following frequency distribution on days absent during a calendar year by employees of a manufacturing
company:
Days Absent Cumulative Number of Employees
0 up to 3 60
3 up to 6 31
6 up to 9 14
9 up to 12 6
12 up to 15 2

How many employees were absent between 3 up to 6 days?

Homework Statement

I am disagreement with my professor (I think... he won't email me back, I guess he's ingoring me) on the answer.

Homework Equations

I believe the answer is 17. He said the answer is 31. I would agree if it didn't say CUMULATIVE at the top. I got an answer wrong on a quiz because I didn't notice it said cumulative at the top. So, it can't be both ways.

The Attempt at a Solution

If it just said "number of employees", I would say 31. But it says cumulative and cumulative, you add each frequency together. Looking at this distribution chart, there are a total of 60 students.

 

[Mark44]

The chart, as shown, raises more questions than it answers.

Can there be fractional parts of days missed?

Does "0 up to 3" mean 0 <= # days missed < 3, where the number of days missed can be fractions of days? If the number of days missed can't be fractional, then the categories overlap, so an employee who misses 3 days would be counted twice.

What does "cumulative number of employees" mean?

How did you get 17 for your answer?

For the table to have any real meaning, the categories have to be non-overlapping, so that if you know how many days an employee missed, there would be no question as to which category the employee would be placed in. This leads me to believe that the first category is 0 days or more, but less than 3 days. The second category would be 3 days or more, but less than 6, and so on. Assuming this is what the categories are, and that the question is "how many employees missed 3 or more days, but less than 6?" the answer would be 31.

My reading of the table is that there are 113 employees in the company, assuming that no employees missed 15 or more days.

 

[Tami]

We worked on setting up frequency distributions. They started like this:

Days Absent Number of employees cumulative number of employees
0 up to 3 29 60
3 up to 6 17 31
6 up to 9 8 14
0 up to 12 4 6
12 up to 15 2 2

3 would only be counted in the 3 up to 6 class. I got 17 because that is the difference in 31 and 14 because the column is marked cumulative. however, normally, the cumulative frequency would go the other way (like the cumulative would start with 29 and the next would be 46 - it would add down not up). So that is why is partly confusing. If you could just look at the distribution chart and pick the number of employees in 3 up to 6, a second grader could do that. It was marked cumulative and that is my only argument. In order for the answer to be 31, the column should be marked number of employees, not cumulative number of employees.

 

[Mark44]

I think you are confusing frequence and cumulative frequency with number of employees. As I understand this problem, it should NOT say "cumulative number of employees." It doesn't make any sense to accumulate employees who are in distinct classes. If the classes overlapped as below, then it would make sense to accumulate them.
0 <= days < 3
0 <= days < 6
0 <= days < 9
etc.

In your problem, the frequencies and cum. frequencies are as in this table:
Absences (days)..No. employees...Freq...Cum. frequency
0 up to 3 ...60......60/113...60/113
3 up to 6 ...31......31/113...91/113
6 up to 9 ...14......14/113...105/113
9 up to 12 ...6.....6/113...111/113
12 up to 15 ...2.....2/113...113/113

 

[statdad]

It seems the faculty member used "Cumulative number of employees" to mean frequency for each class.

 

[Tami]

I agree with the two previous posts 100%. So, what do you think should happen? The columns were labeled "Number of Days Absent" and "Cumulative Number of Employees". The only reason I subtracted to get the total number of the specific class, was because it was marked Cumulative. If it is just frequency, how easy is it to just look at the chart and pick the total. He has the difficulty level as hard.

 

[Mark44]

Your next step should probably be to go talk with your professor. He/she is the only person who can clarify what is meant by this problem.