Data is everywhere — and being able to collect, organise, display and interpret it is one of the most useful skills you'll ever learn! In Grade 6, you'll master the four averages (mean, median, mode, range), read and draw different types of charts, and investigate patterns in data. Time to crack the case!
📊 The Four M's
Mean = sum ÷ count · Median = middle value Mode = most frequent · Range = max − min
🥧 Pie Charts
Each slice = (frequency ÷ total) × 360° All slices sum to 360°!
📈 Line Graphs vs Bar Charts
Line graphs: continuous data (temperature over time) Bar charts: discrete categories
📋 Golden Rules
📐 Mean
Add all values, then divide by how many values there are. Think of it as the "fair share" of the total.
Mean = (sum of all values) ÷ (number of values)
📏 Median
Put values in ORDER first, then find the middle value. If there are two middle values, find their mean.
Odd count → middle value is the median.
Even count → median = (value below middle + value above middle) ÷ 2
🎯 Mode
The value that appears most often. There can be more than one mode — or none if all values appear only once.
Look for repeats. The one (or ones) that repeat most is the mode.
📉 Range
Largest value minus smallest value. The range measures spread, not average — it tells you how spread out the data is.
Range = maximum − minimum
🥧 Pie Charts
Each sector angle = (frequency ÷ total frequency) × 360°. All angles must add up to exactly 360°. Always check your working!
Sector angle = (category count ÷ total count) × 360°
📊 Bar Charts
Bars should be equal width, with gaps between them for discrete (separate) data. Both axes must be clearly labelled with titles and units.
Use bar charts for discrete, categorical data (e.g. favourite colours, types of pet).
📈 Line Graphs
Suitable for continuous data (measurements that change over time). The line between points suggests values in between — so only use a line graph when in-between values make sense.
Use line graphs for data over time (e.g. temperature, height as a child grows).
📋 Frequency Tables
Organise data using tally marks. Each group of five is written as four vertical lines crossed by one diagonal line (||||). The frequency is the count of each category.
Frequency = how many times each value or category appears in the data.
Quick Recap — The Four Averages at a Glance
Average
What it is
How to find it
Mean
The "fair share"
Sum ÷ count
Median
The middle value
Order, then find middle
Mode
Most frequent value
Find what repeats most
Range
Spread of data
Max − Min
Collins Stage 6 — Units 25 & 26: Statistics A & B | FractionRush
🔍 Worked Examples
Follow each step carefully — understanding the method is the key to becoming a Data Detective!
Example 1: Mean, Median, Mode and Range
Data set: 5, 3, 8, 3, 7, 9, 3, 6
Step 1 — Order the data: 3, 3, 3, 5, 6, 7, 8, 9
Step 2 — Mode: 3 (appears 3 times — the most frequent value)
Step 3 — Median: There are 8 values (even), so median = average of 4th and 5th values. 4th value = 5, 5th value = 6 → Median = (5 + 6) ÷ 2 = 5.5
The data is skewed — some high values are pulling the mean above the median. There are likely a few very high scores.
Largest value = 27 → 7 + 20 = 27
Mean = 58 (406 ÷ 7); Median = 58 (sorted: 45, 45, 45, 58, 62, 71, 80); Mode = 45
1/5 → 72 ÷ 360 = 1/5
90° → (15 ÷ 60) × 360 = ¼ × 360 = 90°
Sum = 48 → 6 × 8 = 48
Median = 14° → Sorted: 12, 13, 14, 17, 19; middle value = 14°
The mean is most affected by outliers, because extreme values change the total sum.
90° each → 360° ÷ 4 = 90°
The category with the tallest bar has 35 responses (or 35 in whatever unit the axis represents) — it is the most frequent category.
Collins Stage 6 — Units 25 & 26: Statistics A & B | FractionRush
🏆 Challenge Problems
Show all working. These questions require multiple steps — think carefully before you calculate!
Six friends' heights in cm: 142, 156, 148, 163, 148, 159.
Find the mean, median and mode. Comment on which average best represents the data.
A student's test scores were: 72, 68, 80, 75, 68. She takes one more test.
What score does she need to achieve a mean of 75?
60 people were asked their favourite season: Spring 15, Summer 24, Autumn 12, Winter 9.
Calculate the angle for each sector in a pie chart, and verify they sum to 360°.
A data set has mean = 10, median = 8 and mode = 6. A new value of 6 is added. Describe what happens to each average (mean, median, mode).
A line graph shows monthly sales over 5 months: 120, 145, 130, 160, 175.
Calculate the mean monthly sales and the range.
The mean age of 5 children is 9. When an adult joins the group, the mean becomes 14.
How old is the adult?
Two classes take the same test. Class A (25 students) has a mean score of 72.
Class B (15 students) has a mean score of 80.
Find the combined mean score for all 40 students.
A pie chart shows 3 sectors. One sector is 150°, another is 120°.
Find the third angle. What fraction of the total does each sector represent?
A data set is: 2, 5, 8, x, 12, 15 (in order). The median is 9.
Find the value of x.
A school records books read per student in a month:
0–2 books: 8 students | 3–5 books: 14 students | 6–8 books: 10 students | 9–11 books: 8 students
What is the modal group? Estimate the mean using midpoints.
Challenge Answers
Mean: (142+156+148+163+148+159) ÷ 6 = 916 ÷ 6 ≈ 152.7 cm Median: Sorted: 142, 148, 148, 156, 159, 163 → (148+156) ÷ 2 = 152 cm Mode:148 cm (appears twice) Comment: The mode (148) is slightly below the group centre. Both median and mean (≈152–153) give a fairer picture of the typical height in this group.
Current sum = 72+68+80+75+68 = 363
Required sum for mean of 75 with 6 scores = 6 × 75 = 450
Score needed = 450 − 363 = 87
Mode: stays 6 (adding another 6 reinforces it as most frequent) Median: likely decreases slightly — the new low value shifts the middle downward Mean: decreases — the new value (6) is below the current mean of 10, pulling the average down