S1 Maths - Mean, Median and Mode: Lesson Prep Guide for Tutors (three different averages, outliers, weighted mean)

S1 Maths – Mean, Median and Mode: Lesson Prep Guide for Tutors (three different averages, outliers, weighted mean)

2026-11-14

Tutor lesson-prep guides · Secondary Maths

For one class of eight scores from 9 to 22 the mean is 15.75, the median 15 and the mode 15, close enough that students decide the three ideas are the same. Add a single 30 and the mean rises to 17.33 while the median and mode do not move, and the difference appears by itself.

Objectives — By the end students can: (1) take 9, 12, 15, 15, 15, 18, 20 and 22 and get a mean of 15.75, a median of 15 and a mode of 15, stating that the median needs the data sorted first; (2) add a 30 and get a mean of 17.33 while the median and mode stay at 15, stating that an outlier pulls the mean and not the median; (3) reverse five numbers with a mean of 12 and four known values to get 12, and work out that 20 people averaging 60 with 30 averaging 70 gives a weighted mean of 66.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Adding and dividing	Eight numbers add to 126. What is the average?	126 divided by 8, which is 15.75
Sorting small to large	Put 12, 9, 22 and 15 in order	9, 12, 15, 22
Fractions and decimals	Write 126 divided by 8 as a fraction	63 over 4, which is 15.75

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	Three words for average	Write mean, median and mode on the board and ask which one they normally mean	Name the one they have used
5-15 min	The mean	Add 9, 12, 15, 15, 15, 18, 20 and 22 to get 126, then divide by 8 to get 15.75	Get 126 and 15.75 themselves
15-24 min	The median needs order	Sort first, then take the middle pair 15 and 15 for eight values, giving 15	Say that with eight values you take the fourth and fifth
24-33 min	Add one 30	With nine values the total is 156, so the mean is 17.33; then ask what happens to the median and mode	Get 17.33 and say the median is still 15
33-41 min	Reverse and weight	Five numbers average 12 and four are 10, 11, 13, 14, so find the fifth; then 20 people at 60 with 30 at 70	Get 12 and 66
41-45 min	Exit check	Three oral questions: which value needs sorting, which one an outlier moves, and the reverse step	Answer aloud with a reason

03 Teaching script (read it out)

Scene 1: Act 1: the mean is a fair share

“The mean is the easiest: add everything, then share it out equally. 9, 12, 15, 15, 15, 18, 20 and 22 add to 126, and shared between eight people that is 15.75 each. Picture pouring all eight scores into one jug and pouring eight equal cups back. That is why the mean need not be a score anybody actually got: nobody scored 15.75.”

Students repeat: add then divide, the mean may not exist in the data

Scene 2: Act 2: the median needs a queue

“The median is the one standing in the middle of the queue, so sort first: 9, 12, 15, 15, 15, 18, 20, 22. With eight scores nobody is exactly in the middle, so take the fourth and the fifth, both 15, and average them to 15. With seven scores you take the fourth only, no averaging needed.”

Students repeat: sort first, average the middle pair when the count is even

Scene 3: Act 3: an outlier moves only the mean

“Now a new student joins with 30. The total becomes 156 over nine people, so the mean climbs to 17.33, up by one and a half. The median? After sorting, the fifth value is still 15, untouched. The mode? Still 15, because 15 appears three times. So when a set has an extreme value, the median is the steadier summary. Weighted mean is a different job: 20 people averaging 60 and 30 averaging 70 is not 65, it is (20 x 60 + 30 x 70) divided by 50, which is 66, because the bigger group carries more weight.”

Students repeat: an outlier pulls the mean, not the median

04 Question types and worked steps

Type	Example	Steps	Answer
All three averages	Find the mean, median and mode of 9, 12, 15, 15, 15, 18, 20, 22	(1) Total then divide by n (2) sort and take the middle (3) count frequencies (4) state all three	15.75, 15 and 15
Add an outlier	How do the three change when a 30 is added?	(1) n increases by one (2) total increases by 30 (3) re-sort (4) compare the three	17.33, 15 and 15
Reverse the mean	Five numbers average 12 and four are 10, 11, 13 and 14	(1) Total is 5 times 12 (2) subtract the four known values (3) that is the fifth (4) check	60 minus 48 is 12
Weighted mean	20 people average 60 kg and 30 average 70 kg. What is the combined mean?	(1) Multiply each mean by its count (2) add the totals (3) divide by all 50 (4) never average two means directly	(1200 + 2100) divided by 50 is 66 kg

Sanity check (teach this): Reasonableness checks: a mean must sit between the smallest and largest values, and 15.75 lies between 9 and 22; a median must come from the middle of the sorted list, and 15 does for eight values; a mode must actually occur, and 15 occurs three times; adding an outlier moves the mean towards it, so 17.33 above 15.75 is right; a weighted mean must lie between 60 and 70, and 66 does, while 65 means the weighting was skipped; a reversed value must be a plausible score, and 12 is neither negative nor above 22.

05 Independent practice (3 questions)

Question	Answer	What to watch
Find all three averages of 3, 5, 5, 8, 9, 12, 15	Mean 57 over 7, about 8.14, median 8, mode 5	Three different values, so answering 8 for all three means the ideas are still merged
Ten students average 48 kg and an eleventh joins at 59 kg	(480 + 59) divided by 11 is 49 kg	Forgetting to multiply 48 by 10 gives (48 + 59) divided by 2
Five numbers average 12 and four are 10, 11, 13, 14. Find the fifth	5 x 12 minus 48 is 12	Both the 60 and the 48 must be written down

06 Common mistakes and what to say

Mistake	Student writes	Say this
No sorting before the median	“The middle of 9, 12, 15, 15, 15, 18, 20, 22 is the fifth value, so 15.”	“Without sorting, the middle is luck. In the order 12, 15, 15, 18, 20, 15, 22, 9 the middle pair is 20 and 15, averaging 17.5, which is wrong. Always sort first.”
Reading the mode as the biggest number	“The mode is 22 because it is the largest.”	“The mode is the value that appears most often, not the largest. 15 appears three times and nothing else appears more than twice, so the mode is 15.”
Averaging two means directly	“Two classes average 60 and 70, so together it is 65.”	“The groups differ in size, 20 and 30. Use (20 x 60 + 30 x 70) divided by 50, which is 66. The bigger group pulls the answer towards 70.”
Skipping the total when reversing	“Five numbers average 12, so subtract 48 from 12.”	“The total is 5 times 12, which is 60, not 12. 60 minus 48 is 12, and the fifth number is 12. Subtracting 48 from 12 gives a negative score, which is immediately impossible.”

07 Homework (paper, section and question numbers)

Redo Act 1: take your last dictation scores and find the mean, median and mode — Chapter practice, question 1
Find one news report that uses an average and say whether an outlier could distort it — Chapter practice, question 2
Preview: take the mean heights of the boys and the girls in your class and work out the weighted mean for the whole class — Chapter practice, question 3

08 Exit check (last 5 minutes)

Question	Answer	Decision
Which of the three averages needs the data sorted first?	The median; the mode only needs counting	Saying all three means Act 2 again
When a very large value is added, which average moves?	The mean moves, while the median and usually the mode stay	Saying all three move means Act 3 again
20 people average 60 and 30 average 70. What is the combined mean?	66, weighted by the group sizes	An answer of 65 means Act 3 again

09 Tutor FAQ

Can there be more than one mode?

Yes. If two values occur equally often it is called bimodal and both must be stated, never just one.

Should the mean be a decimal or a fraction?

Either, but stay consistent. 15.75 and 63 over 4 are the same value, and match whatever decimal place the question asks for.

Why teach the weighted mean in S1 if the exam only asks for the mean?

The exam mixes them: two classes combined, or boys and girls together, is a weighted mean. Without it students keep writing (a + b) divided by 2.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.