Interpreting a graph

[Little_Louis]

Hello this is my first post - thank you for your help in advance. I recently completed an online test. This was one of the questions and it baffled me. I have attempted to recreate the question in excel. Please can you help.

The Test Problem

113 students are enrolled on a course of 24 lectures:

• Fifteen students attended all lectures
• 98 were absent for between 1 and 12 of the lectures

Frequency Distribution of no of absences for each student

x axis = absences, y axis = count

How many of the following can be deduced just from the data in the chart

1. The mean number of absences per student was 6
2. At least half the lectures did not have full attendance
3. The most frequent number of students attending a lecture was 91
4. One lecture was attended by only 15 students

I then quickly calculated what I thought was the mean given the graph. I got a mean of 3.14 using my own figures as per my table below.

Absence	Frequency
0	15
1	16
2	20
3	21
4	16
5	9
6	6
7	3
8	2
9	1
10	1
11	1
12	2

I then looked at the options 1 to 4 and thought 'I don't think any of those are correct'. However the answer must be a number between 1 and 4 correct options.

 

[lev888]

6 is the median. Are you sure the question was about the mean?

 

[Dr.Peterson]

Hello this is my first post - thank you for your help in advance. I recently completed an online test. This was one of the questions and it baffled me. I have attempted to recreate the question in excel. Please can you help.

The Test Problem

113 students are enrolled on a course of 24 lectures:

• Fifteen students attended all lectures
• 98 were absent for between 1 and 12 of the lectures

Frequency Distribution of no of absences for each student
View attachment 31829
x axis = absences, y axis = count

How many of the following can be deduced just from the data in the chart

1. The mean number of absences per student was 6
2. At least half the lectures did not have full attendance
3. The most frequent number of students attending a lecture was 91
4. One lecture was attended by only 15 students

I then quickly calculated what I thought was the mean given the graph. I got a mean of 3.14 using my own figures as per my table below.

Absence	Frequency
0	15
1	16
2	20
3	21
4	16
5	9
6	6
7	3
8	2
9	1
10	1
11	1
12	2

I then looked at the options 1 to 4 and thought 'I don't think any of those are correct'. However the answer must be a number between 1 and 4 correct options.

You're right about the mean (and the median is 3).

So #1 is false.

But the other statements are about lectures, not students, so they take a little more thought than initially appears; what ideas do you have on each of them?

For #2, what is the least number of lectures that could have had less than full attendance? (In other words, what is the greatest number that could have had full attendance?)

I have not worked out all the answers myself. What is this test for? The more I think about it, the harder I realize it is!

 

[blamocur]

My reading of the problem implies that only #2 can be deduced. In particular, my mean value is 3.14159... (almost [imath]\pi[/imath]).

 

[Steven G]

We are told that 2 student missed exactly 12 classes. Since there were 24 classes, that means that these two students went to 12 classes (half of them).
Now all the other students attended more than 12 classes. It could be the case where all 24 students attended the same12 classes. So it is possible that all 24 students attended exactly half the classes. If things did not line up so well, then less than half the classes had all 24 students. #2 is valid.

 

[Little_Louis]

6 is the median. Are you sure the question was about the mean?

@lev888 yes, it's exactly the same, I took a screenshot of the question. I've recreated it, and added a frequency table.

 

[Little_Louis]

You're right about the mean (and the median is 3).

So #1 is false.

But the other statements are about lectures, not students, so they take a little more thought than initially appears; what ideas do you have on each of them?

For #2, what is the least number of lectures that could have had less than full attendance? (In other words, what is the greatest number that could have had full attendance?)

I have not worked out all the answers myself. What is this test for? The more I think about it, the harder I realize it is!

@Dr.Peterson So for this question, between 1 to 4 of the options had to be correct. But the way it's worded, it's as if all of them are correct, but which one can you deduce from this graph alone, without seeing the underlying data. Now that shredded my head. I then chose no 2. However, I then thought, it doesn't actually tell us which lectures out of the 24, they attended, just the absences.

I also thought about the scoring on this. So 3 if it's correct, -1 if it's wrong and 0 no attempt. I chose 0 because I didn't want to guess and lose points. Also, it's a question from the government statistician test.

 

[Dr.Peterson]

So for this question, between 1 to 4 of the options had to be correct. But the way it's worded, it's as if all of them are correct, but which one can you deduce from this graph alone, without seeing the underlying data. Now that shredded my head. I then chose no 2. However, I then thought, it doesn't actually tell us which lectures out of the 24, they attended, just the absences.

Each option might be either provably true, or potentially true but needing additional information to know that, or provably false.

We have to deduce facts about attendance at each lecture from the given facts about students.

I also thought about the scoring on this. So 3 if it's correct, -1 if it's wrong and 0 no attempt. I chose 0 because I didn't want to guess and lose points.

You found that #1 is false, and @Steven G has shown that #2 is provably true. I haven't looked deeply into the rest, but the answer so far appears to be either 1, 2, or 3. (What is your expected value if you give one of those answers?)

 

[Little_Louis]

Each option might be either provably true, or potentially true but needing additional information to know that, or provably false.

We have to deduce facts about attendance at each lecture from the given facts about students.


You found that #1 is false, and @Steven G has shown that #2 is provably true. I haven't looked deeply into the rest, but the answer so far appears to be either 1, 2, or 3. (What is your expected value if you give one of those answers?)

It's a right or wrong answer so it's either 3 (chose all the correct options) or -1 (did not choose all correct options). That's why I didn't answer this question, too nervous over the point loss.

 

[Little_Louis]

@Dr.Peterson @Steven G @blamocur @lev888 thank you very much for your help today.