Problem with Averages

G

garfas

New Member
Joined
Oct 22, 2018
Messages
2
Hi All,

I'm working on this problem about test scores and I'm trying to figure out why I'm getting a different number when I get a mean of pupil grade score percentages versus when I do the other way by getting a mean for each individual test and then averaging that? I have noticed that if the the number of questions in each test are equal, I don't have this problem (see example 2) Any help greatly appreciated? Gar



EXAMPLE1




Out ofTOTAL
Test
Test
EXAMPLE2




Out ofTOTAL
Test
Test

<colgroup><col style="width:48pt" width="64" span="2"> <col style="mso-width-source:userset;mso-width-alt:3145;width:65pt" width="86"> <col style="mso-width-source:userset;mso-width-alt:3474;width:71pt" width="95"> <col style="mso-width-source:userset;mso-width-alt:2925;width:60pt" width="80"> <col style="width:48pt" width="64" span="2"> <col style="mso-width-source:userset;mso-width-alt:4461;width:92pt" width="122"> <col style="mso-width-source:userset;mso-width-alt:1170;width:24pt" width="32"> <col style="width:48pt" width="64" span="3"> </colgroup><tbody>
[TD="width: 64"][/TD]
[TD="width: 64"][/TD]
[TD="class: xl63, width: 86"]Test1
[/TD]
[TD="class: xl63, width: 95"]Test2
[/TD]
[TD="class: xl63, width: 80"]Test3
[/TD]
[TD="width: 64"][/TD]
[TD="width: 64"][/TD]
[TD="width: 122"][/TD]
[TD="width: 32"][/TD]
[TD="width: 64"][/TD]
[TD="width: 64"][/TD]
[TD="width: 64"][/TD]

[TD="class: xl64"] 12
[/TD]
[TD="class: xl64"]20[/TD]
[TD="class: xl64"]10[/TD]

[TD="class: xl64"]Out of
[/TD]
[TD="class: xl64"] Pupil Avg %
[/TD]

[TD="class: xl66"]Pupil1
[/TD]
[TD="class: xl67"]12[/TD]
[TD="class: xl68"]10[/TD]
[TD="class: xl68"]9[/TD]
[TD="class: xl68"]31[/TD]
[TD="class: xl69"]42[/TD]
[TD="class: xl65, align: right"]73.809523810%[/TD]

[TD="class: xl66"]Pupil2
[/TD]
[TD="class: xl70"]8[/TD]
[TD="class: xl64"]12[/TD]
[TD="class: xl64"]7[/TD]
[TD="class: xl64"]27[/TD]
[TD="class: xl71"]42[/TD]
[TD="class: xl65, align: right"]64.285714286%[/TD]

[TD="class: xl66"]Pupil3
[/TD]
[TD="class: xl70"]12[/TD]
[TD="class: xl64"]14[/TD]
[TD="class: xl64"]8[/TD]
[TD="class: xl64"]34[/TD]
[TD="class: xl71"]42[/TD]
[TD="class: xl65, align: right"]80.952380952%[/TD]

[TD="class: xl66"]Pupil4
[/TD]
[TD="class: xl70"]12[/TD]
[TD="class: xl64"]14[/TD]
[TD="class: xl64"]9[/TD]
[TD="class: xl64"]35[/TD]
[TD="class: xl71"]42[/TD]
[TD="class: xl65, align: right"]83.333333333%[/TD]

[TD="class: xl66"]Pupil5
[/TD]
[TD="class: xl70"]8[/TD]
[TD="class: xl64"]8[/TD]
[TD="class: xl64"]8[/TD]
[TD="class: xl64"]24[/TD]
[TD="class: xl71"]42[/TD]
[TD="class: xl65, align: right"]57.142857143%[/TD]

[TD="class: xl66"]Pupil6
[/TD]
[TD="class: xl72"]12[/TD]
[TD="class: xl73"]13[/TD]
[TD="class: xl73"]9[/TD]
[TD="class: xl73"]34[/TD]
[TD="class: xl74"]42[/TD]
[TD="class: xl65, align: right"]80.952380952%[/TD]

[TD="class: xl66"]Avg[/TD]
[TD="align: right"]10.66666667[/TD]
[TD="align: right"]11.83333333[/TD]
[TD="class: xl75, align: right"]8.3333333[/TD]
[TD="class: xl64"]30.83333[/TD]

[TD="class: xl78, align: right"] 73.4126984%
[/TD]

[TD="class: xl66, colspan: 2"]Mean Pupil Avg %[/TD]

[TD="class: xl66"]Avg %[/TD]
[TD="align: right"]0.888888889[/TD]
[TD="align: right"]0.591666667[/TD]
[TD="align: right"]0.83333333[/TD]

[TD="class: xl79"]Mean
[/TD]
[TD="class: xl66, colspan: 2"]Test Avg %
[/TD]
[TD="class: xl78, align: right"] 77.1296296%
[/TD]

[TD="class: xl76, colspan: 3"] Why are these Averages different?
[/TD]

[TD="class: xl63"]Test1
[/TD]
[TD="class: xl63"]Test2
[/TD]
[TD="class: xl63"]Test3
[/TD]

[TD="class: xl64"][/TD]

[TD="class: xl64"] 14
[/TD]
[TD="class: xl64"] 14
[/TD]
[TD="class: xl64"] 14
[/TD]

[TD="class: xl64"]Out of[/TD]
[TD="class: xl64"] Pupil Avg %
[/TD]

[TD="class: xl66"]Pupil1
[/TD]
[TD="class: xl67"]12[/TD]
[TD="class: xl68"]10[/TD]
[TD="class: xl68"]9[/TD]
[TD="class: xl68"]31[/TD]
[TD="class: xl69"]42[/TD]
[TD="class: xl65, align: right"]73.809523810%[/TD]

[TD="class: xl66"]Pupil2
[/TD]
[TD="class: xl70"]8[/TD]
[TD="class: xl64"]12[/TD]
[TD="class: xl64"]7[/TD]
[TD="class: xl64"]27[/TD]
[TD="class: xl71"]42[/TD]
[TD="class: xl65, align: right"]64.285714286%[/TD]

[TD="class: xl66"]Pupil3
[/TD]
[TD="class: xl70"]12[/TD]
[TD="class: xl64"]14[/TD]
[TD="class: xl64"]8[/TD]
[TD="class: xl64"]34[/TD]
[TD="class: xl71"]42[/TD]
[TD="class: xl65, align: right"]80.952380952%[/TD]

[TD="class: xl66"]Pupil4
[/TD]
[TD="class: xl70"]12[/TD]
[TD="class: xl64"]14[/TD]
[TD="class: xl64"]9[/TD]
[TD="class: xl64"]35[/TD]
[TD="class: xl71"]42[/TD]
[TD="class: xl65, align: right"]83.333333333%[/TD]

[TD="class: xl66"]Pupil5
[/TD]
[TD="class: xl70"]8[/TD]
[TD="class: xl64"]8[/TD]
[TD="class: xl64"]8[/TD]
[TD="class: xl64"]24[/TD]
[TD="class: xl71"]42[/TD]
[TD="class: xl65, align: right"]57.142857143%[/TD]

[TD="class: xl66"]Pupil6
[/TD]
[TD="class: xl72"]12[/TD]
[TD="class: xl73"]13[/TD]
[TD="class: xl73"]9[/TD]
[TD="class: xl73"]34[/TD]
[TD="class: xl74"]42[/TD]
[TD="class: xl65, align: right"]80.952380952%[/TD]

[TD="class: xl66"]Avg[/TD]
[TD="align: right"]10.66666667[/TD]
[TD="align: right"]11.83333333[/TD]
[TD="class: xl75, align: right"]8.3333333[/TD]
[TD="class: xl64"]30.83333[/TD]

[TD="class: xl77, align: right"] 73.4126984%
[/TD]

[TD="class: xl66, colspan: 2"]Mean Pupil Avg %[/TD]

[TD="class: xl66"]Avg %[/TD]
[TD="align: right"]0.761904762[/TD]
[TD="align: right"]0.845238095[/TD]
[TD="align: right"]0.5952381[/TD]

[TD="class: xl79"]Mean[/TD]
[TD="class: xl66, colspan: 2"]Test Avg %
[/TD]
[TD="class: xl77, align: right"] 73.4126984%
[/TD]

[TD="class: xl76, colspan: 3"] Ok when test question numbers equal
[/TD]

</tbody>
 

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Hi there.

If youre worried that excel is getting it wrong, dont be. The calculations come out differently because of what it is that you are averaging. Averaging averages can and does reult in this kind of apparent anomaly.
 
Last edited:
Upvote 0
Ok. I've been doing some research on this. Now I'm wondering, as the test question number is different, if I should be using weighted averages using SUMPRODUCT
 
Upvote 0
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