Comparing the mean, median, mode and range
Six groups of students - P, Q, R, S, T and U – all sit the same test. The test is marked
out of 20. There are four students in each group.
The table below shows the analysis of each group’s results.
Group
P
Q
R
S
T
U
Mean
14
14
15
15
15
14
Median
13
14
14
18
14
14
Mode
11
-
14
-
14
-
Range
8
8
8
16
6
4
Using the information in the table, complete the statements below in
order to compare ...
1. groups Q and R
2. groups P, Q and U
3. groups R, S and T.
 Use all of these statements each time to give a full comparison:

On average, the [mean/median/mode/range] shows that …

Using the [mean/median/mode/range], the spread of the results shows …

Overall the most successful group was … because …
Extension challenge
Calculate the possible test results for each student in each group. Some
groups may have more than one possible solution.
(HINT: to start, work out each group’s total score.)
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Comparing the mean, median, mode and range
Five groups of students – V, W, X, Y and Z – all sit the same test. The test is marked out
of 20. There are five students in each group.
The table below shows the analysis of each group’s results.
Group
V
W
X
Y
Z
Mean
14
15
13
15
15
Median
12
16
15
16
14
Mode
12
-
15
-
14
Range
7
9
15
11
13
Using the information in the table, write a paragraph to compare how
each group performed in the test. Use all of these statements to
give a full comparison:
–

On average, the [mean/median/mode/range] shows that …

Using the [mean/median/mode/range], the spread of the results shows …

Overall the most successful group was … because …

Overall the least successful group was … because …
Extension challenge
Calculate the possible test results for each student in each group. Some
groups may have more than one possible solution.
(HINT: to start, work out each group’s total score.)
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Comparing the mean, median, mode and range
P, Q, R, S, T & U - possible answers
Comparing Q and R
 On average, the mean shows that group R was more successful.
 Using the range, the spread of the results shows that both groups were
equally consistent.
 Overall the most successful group was R because its mean score was
higher.
Comparing P, Q and U
 On average, the mean shows that all three groups performed the same but
Q and U had a higher median so therefore performed better than group P.
 Using the range, the spread of the results shows group U’s results were
most consistent. P and Q were as consistent as each other.
 Overall the most successful group was U because it had the joint highest
median and its scores were the most consistent. However, P had the joint
highest median and a larger spread, meaning one of its students may have
had the highest score overall.
Comparing R, S and T
 On average, the mean shows that all three groups performed the same.
The median shows that S performed better than R and T.
 Using the range, the spread of the results shows group S was very
inconsistent. However group S had the highest median, perhaps showing
that three members performed well, with one student getting an
abnormally low mark. Group T was more consistent as its range was
smaller than the other two groups.
 Overall the most successful group was S because their median score was
much higher than the others. In this case, the range may be confusing as
it is affected by extreme values.
Extension challenge – possible solutions
Group
Marks
P
11
11
15
19
Q
10
12
16
18
R
12
14
14
20
S
4
17
19
20
T
13
14
14
19
U
12
13
15
16
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Comparing the mean, median, mode and range
W, X, Y and Z – possible answers

On average, the mean shows that groups W, Y and Z were more successful
because their means were the highest. The median shows that W and Y
performed better than Z.

Using the range, the spread of results shows that group V was the most
consistent. The least consistent group was X.

Overall the most successful group was W because, although its mean and
median score was the same as Y, the range shows that the group as a
whole was more consistent. However, it is likely that the individual
student with the highest mark would appear in one of the groups with a
larger spread.

Overall the least successful group was X because its mean score was the
lowest. The range also shows X to be the least consistent, meaning this
group would have had one student with a very low score.
Extension challenge – possible solutions
Group
Marks
V
12
12
12
15
19
W
9
15
16
17
18
X
2
15
15
16
17
Y
8
14
16
18
19
Z
7
14
14
20
20
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