S3 Maths | Central Tendency and Data Display Lesson Prep Guide (for tutors)

S3 Maths | Central Tendency and Data Display Lesson Prep Guide (for tutors) | Mean, median, mode and stem-and-leaf

2026-11-09

Tutor lesson-prep guides · Secondary Maths (DSE)

The three averages are not three formulas side by side but three questions: which value best represents the data, and which one gives way first when the data changes.

Objectives — Students can: (1) compute the mean, median and mode of a data set and say when each is most reliable; (2) use a weighted mean for scores with different weights; (3) read a stem-and-leaf plot and predict how each average moves when an outlier is added, scoring at least 11 of 14 in the diagnostic.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Addition and division	What is the total of 12, 15, 15, 18, 20, 22 and 25?	127
Ordering	Put those seven numbers in order; which one is in the middle?	18
Percentages	What is 40 percent of 65?	26

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-6 min	Three questions, not three formulas	Ask of the same seven numbers: which is most representative, which is in the middle, which appears most	Give three answers
6-16 min	Mean and weighted mean	127 divided by 7 is 18.14; then blend a 40 percent test at 65 with a 60 percent exam at 80 to get 74	Compute the weighted mean
16-30 min	Median and mode	The fourth value in order is 18; 15 appears twice so the mode is 15	Say why the mean is not the median
30-42 min	Stem-and-leaf	Stem 1 with leaves 2, 5, 5, 8 and stem 2 with 0, 2, 5 gives all 7 values at a glance	Draw the plot and read it back
42-56 min	14-question diagnostic	Four question types, marked on the spot: 11 right, 3 wrong	Independent work
56-60 min	Exit check	Three oral questions; any miss points to the stage to reteach	Oral answers

03 Teaching script (read it out)

Scene 1: Ask what represents before quoting formulas

Mean, median and mode look like three formulas but they answer three different questions: the mean answers what each person gets if the total is shared equally, the median answers who is in the middle, and the mode answers what is most common. For the same seven numbers the mean is 18.14, the median is 18 and the mode is 15; all three are correct because the questions differ.
Teaching move: require one written line before any calculation stating which of the three is being asked for.

Students do: describe 12, 15, 15, 18, 20, 22, 25 with all three averages and say which one best represents the set, with a reason.

Scene 2: Mean: total divided by count

The mean is the total divided by the number of values: 127 over 7 gives 18.14 to two decimal places. Three places where marks go: one value left out of the total, dividing by the wrong count, and inconsistent decimal places.
A weighted mean is the same line plus weights: a 40 percent test at 65 and a 60 percent exam at 80 give 0.4 times 65 plus 0.6 times 80, which is 74. Weights must total 100 percent or be normalised first.

Students do: change the weights to 30 and 70 percent, recompute, and explain why the mark rises.

Scene 3: Median and mode: position and frequency

The median depends on position, not size. Sorted, the fourth of seven values is 18; with eight values the median is the average of the fourth and fifth. The mode is the most frequent value, so 15 wins with two appearances; a set can have two modes or none.
Teaching move: make students draw a numbered position line before circling the middle, rather than guessing the centre.

Students do: add 40 to the data, recompute all three and say which one moved most.

Scene 4: Adding an outlier: three different reactions

Adding 40 raises the total from 127 to 167 and the count from 7 to 8, so the mean rises to 20.875. The fourth and fifth values are now 18 and 20, so the median becomes 19, while the mode stays 15. The mean is pulled hardest, the median is the most stable, and the mode only counts appearances.
Teaching move: fix one comparison sentence (“the mean rose most, the median rose slightly, the mode did not move”) as the standard answer form.

Students do: replace 40 with 100, predict all three movements first, then compute to check.

04 Question types and worked steps

Type	Example	Steps	Answer
Three averages	12, 15, 15, 18, 20, 22, 25	Sort first, then total over count; median takes the middle position; mode counts appearances	mean 18.14, median 18, mode 15
Weighted mean	40 percent test at 65, 60 percent exam at 80	Multiply each score by its weight and add, after checking the weights total 100	74
Stem-and-leaf reading	Stem 1: 2, 5, 5, 8; stem 2: 0, 2, 5	The stem is the tens digit, the leaf the units digit; read row by row	7 values, mode 15
Effect of a change	What happens after adding 40	Recompute the total for the mean; re-sort for the median; recount for the mode	20.875, 19, 15

Sanity check (teach this): Sanity checks: the mean always lies between the smallest and largest value; the median is usually one of the values; a set can have more than one mode; weights must add to 100 percent; 11 out of 14 is 78 percent, not 11 percent.

05 Independent practice (3 questions)

Question	Answer	What to watch
Three averages on three sets	Seven values, eight values, one set with repeats	Did they sort first
Two weighted means	40 and 60 percent, then 30 and 70 percent	Do the weights total 100 percent
Two stem-and-leaf items	Read data from a plot, then draw a plot	Are stem and leaf swapped

06 Common mistakes and what to say

Mistake	Student writes	Say this
Mean written as median	Labelling 18.14 as the median	18.14 shares the total among seven people; the median only looks at the middle position, so they answer different questions.
No sorting	Taking the fourth listed value as the median	The median assumes sorted data; the fourth listed value is only the fourth in the original order.
Miscounting the mode	Calling 18 the mode	15 appears twice and 18 only once; the mode is the most frequent value, not the middle one.
Weights not totalling 100	Adding 40 and 60 then dividing by 2	40 plus 60 is already 100 percent, so add the weighted parts directly and do not divide again.

07 Homework (paper, section and question numbers)

Secondary maths chapter index — All chapters in one place
Master prep guide index — Compare related chapters
Redo this chapter — Redo diagnostic questions 1 to 7, stating which average is being asked each time

08 Exit check (last 5 minutes)

Question	Answer	Decision
Median of the seven values	18	Answering 18.14 means mean and median are confused; reteach stage two
Mean after adding 40	20.875	Answering 18.14 means the total was not recomputed; reteach stage four
Which value is the mode	15	Answering 18 means appearances were not counted; reteach stage three

09 Tutor FAQ

Must all three averages be computed every time?

The question usually names one; if it asks which best represents the data, compute all three and justify the choice in one sentence.

How many decimal places for the mean?

Two unless stated, and say so; for integer data, leaving the fraction 127/7 is also accepted.

How does a stem-and-leaf plot differ from a bar chart?

The plot keeps every original value while a bar chart keeps only group frequencies, so only the plot can give a median.

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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.