DeepMaths Junior

Junior Maths Book 1 AI Learning System

For Years 7-9 - Numbers & Statistics

Chapter 7: Averages, Quartiles and Spread

Averages, Quartiles and Spread

Use statistics to describe both the centre and spread of data, then interpret what those values mean.

Junior Maths Book 1 pages 120-1419 minutes

AI teacher

Start the short explanation, then use the visual model and practice before returning to the workbook.

Voice: Browser voice

Workbook pages

Junior Maths Book 1 pages 120-141

Calculate and interpret mean, median, mode, range, quartiles, IQR, combined mean, box plots and grouped-data estimates.

AI explanation

The AI teacher compares the mean, median and mode as different summaries of centre. Range and IQR describe spread. Box plots are introduced as a compact five-number summary.

  1. 1The mean shares the total equally.
  2. 2The median is the middle after sorting.
  3. 3The mode is the most common value.
  4. 4Range and IQR describe spread.
  5. 5A box plot shows median, quartiles and extremes.

Animated teaching

See the method

Data cards sort into order, median and quartiles drop into place, then a box-and-whisker plot is drawn from the five-number summary.

Box plot showing minimum, quartiles, median and maximum01020304050minQ1medianQ3max

Why this method works

  • Different averages answer different questions about centre.
  • The IQR focuses on the middle half of the data, so it is less affected by extremes.
  • Combined mean works by combining totals, not by averaging the two means unless group sizes are equal.

Common mistakes

  • Finding the median before ordering the data.
  • Averaging two means without considering sample sizes.
  • Confusing range with IQR.
  • Reading a box plot as if the box height mattered.

Multiple methods

  • Mean can be found from raw data, frequency tables or grouped estimates.
  • Quartiles can be located by splitting ordered data or by reading a box plot.
  • Grouped mean can be estimated with midpoints and frequencies.

Worked examples

Median and IQR

Find the median and IQR of 3, 7, 8, 10, 12, 15, 18.

Method: Order the data and locate the quartiles.

  1. 1.The data is already ordered.
  2. 2.The median is the 4th value: 10.
  3. 3.Lower half is 3, 7, 8, so Q1 = 7.
  4. 4.Upper half is 12, 15, 18, so Q3 = 15.
  5. 5.IQR = Q3 - Q1.

Answer: Median = 10, IQR = 8

Combined mean

Group A has 12 students with mean 8. Group B has 18 students with mean 11. Find the combined mean.

Method: Combine totals, then divide by total frequency.

  1. 1.Total for A = 12 x 8 = 96.
  2. 2.Total for B = 18 x 11 = 198.
  3. 3.Combined total = 294.
  4. 4.Total students = 30.

Answer: 9.8

Interactive practice

Try before you look

0/3 correct, 0 answered

Question 1

Find the median of 9, 2, 8, 5, 1.

Question 2

If Q1 = 12 and Q3 = 29, what is the IQR?

Question 3

Why is a grouped-data mean an estimate?

Review prompt

Explain when the median might be more useful than the mean.

Write a two-sentence answer in your notebook before marking the workbook section complete.

Challenge question

Two classes have means 62 and 70. The first class has 20 students and the second has 30 students. Explain why the combined mean is not 66, then find it.

Hint: Use total marks, not the average of the two averages.