Primary 6 Maths | Median, Mode and Mean Lesson-Prep Guide (for tutors) | 45-minute flow, teaching script, common errors

2026-11-15

Tutor lesson-prep guides · Primary Maths

Median, mode and mean are three different representative values, so one question can honestly have three different answers. Pupils need the choosing rule more than the three formulas: mean when the values are close together, median when there is an outlier, mode when the question asks what is most common.

Objectives — By the end of the lesson the pupil can: (1) sort a data set and find the median, including the even-count case where the two middle values are averaged; (2) find the mode and say that a set may have two modes or none; (3) explain that an outlier moves the mean but barely moves the median; (4) choose a representative value for a real question and justify the choice.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Ordering numbers	puts 9, 3, 7, 5 and 1 in order	writes 1, 3, 5, 7, 9
Odd and even counts	says which item is the middle of seven	answers the fourth
Finding a mean	averages 4, 6, 8 and 10	adds to 28, then divides by 4 to get 7

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0–6 min	Entry check	sets three quick items and watches each one	answers aloud and orders once
6–16 min	Median: queue up, then take the middle	lines up five scores and points at the middle	names the middle value
16–24 min	Even counts and the mode	models 12, 15, 18, 20, 22 and 25	writes 18 plus 20, divided by 2
24–33 min	The outlier experiment	adds a score of 100 and compares	says the mean rose and the median barely moved
33–41 min	Independent practice	reads the questions only	works the three items alone
41–45 min	Exit check	collects and marks at once	says which step went wrong

03 Teaching script (read it out)

Scene 1: Act 1: The median is whoever stands in the middle of the queue

“The median is not calculated, it is lined up. Five scores 78, 85, 90, 87, 62 go from smallest to largest: 62, 78, 85, 87, 90. The one standing exactly in the middle is 85, so the median is 85. Why sort? Because the middle means the middle in order of size, not the middle of the page. Without sorting you are just picking a number that happens to sit in the centre.”

If five numbers are not sorted and you take the third one, what can go wrong?

Scene 2: Act 2: Even counts need two values, and the mode is simply the most frequent

“Six values 12, 15, 18, 20, 22, 25 leave no single number in the middle: 18 and 20 stand there together. Average the pair: 18 plus 20 is 38, divided by 2 is 19. The mode is easier: whichever value appears most often. In 4, 4, 6, 7, 7, 7, 9 the 7 appears three times, so 7 is the mode. Two cautions: if every value appears once there is no mode, and if two values tie for most frequent you report both.”

What is the mode of 2, 3, 3, 5, 5 and 8?

Scene 3: Act 3: Why we need three representative values

“Seven values 10, 12, 13, 14, 15, 16, 90 give a mean of 170 divided by 7, about 24.29, but a median of 14. The 90 is an outlier: it drags the mean up while the median hardly moves, because the median only cares about position. That is why salaries and flat prices are quoted as medians, why a class total is quoted as a mean, and why shops care about the mode. None of the three is wrong; they answer different questions.”

If a few values are unusually large, would you use the mean or the median to describe the typical case?

04 Question types and worked steps

Type	Example	Steps	Answer
Median with an odd count	median of 78, 85, 90, 87, 62	sort to 62, 78, 85, 87, 90; take the third	85
Median with an even count	median of 12, 15, 18, 20, 22, 25	average the middle pair 18 and 20	19
Finding the mode	mode of 4, 4, 6, 7, 7, 7, 9	count appearances; 7 appears three times	7
Comparing with an outlier	mean and median of 10, 12, 13, 14, 15, 16, 90	mean is 170 divided by 7; median is the fourth	about 24.29 and 14

Sanity check (teach this): Three checks: the median must be the value in position (n plus 1) divided by 2 after sorting, never a value picked by eye; the median must sit between the smallest and largest value; and when the mean and the median are far apart, look back at the data for an outlier.

05 Independent practice (3 questions)

Question	Answer	What to watch
Find the median of 9, 3, 7, 5 and 1.	5	whether the pupil sorted to 1, 3, 5, 7, 9 before taking the middle
Find the mode of 2, 3, 3, 4, 4, 4, 5 and 5.	4	whether the pupil counted three 4s instead of spotting two 5s
Are the median and the mean of 90, 80, 70 and 60 the same?	both 75	whether the pupil sees that symmetric data makes them equal

06 Common mistakes and what to say

Mistake	Student writes	Say this
Taking the middle without sorting	calls 90 the median of 78, 85, 90, 87, 62	The median is the middle of the queue, not the middle of the page. Sort first.
Reporting one of the two middle values	answers 18 for 12, 15, 18, 20, 22, 25	There are two in the middle, so average them.
Confusing mode with median	calls 7 the median	The mode is the most frequent value, not the middle one.
Inventing a mode	reports a mode when every value appears once	If every value appears once, say there is no mode.

07 Homework (paper, section and question numbers)

Primary 6 maths paper 1: data handling section — Section D, questions 1 to 4

08 Exit check (last 5 minutes)

Question	Answer	Decision
Find the median of 45, 52, 58, 61, 67, 72 and 88.	61	if wrong, reteach Act 1
Find the mode of 1, 2, 2, 3, 5, 5, 5 and 8.	5	if wrong, reteach counting appearances
Find the median and the mean of 4, 6, 8 and 10.	both 7	if wrong, reteach the even-count case

09 Tutor FAQ

Where do the median and the mode sit in the Primary 6 syllabus?

They belong to data handling, taught alongside the mean, bar charts and line graphs. This guide spends 45 minutes on telling the three representative values apart.

Is 45 minutes enough?

Yes. The flow gives 27 minutes to explanation and modelling, 8 to independent practice and 4 to the exit check. If the entry check fails, repair ordering first.

Is there a matching practice paper?

Yes. The homework links straight to the TutorZone Primary 6 maths paper, which carries answers for immediate checking.

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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.

Practice papers　Paper 1 (basics)　·　Paper 2 (intermediate)　·　Paper 3 (challenge)　·　Paper 4 (error clinic)