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Year 11 Maths

Data Types and Displays

Classify data as categorical or numerical, and represent data using histograms, box plots, and stem-and-leaf plots.

Types of Data

Data can be broadly classified into two categories. Choosing the correct data type determines which statistical displays and measures are appropriate.

Categorical Data

Data that falls into categories or groups. Cannot be meaningfully averaged.

Nominal: No natural order (e.g., eye colour, favourite sport)
Ordinal: Has a natural order (e.g., rating 1-5, education level)

Numerical Data

Data that is measured or counted. Can be averaged.

Discrete: Countable values (e.g., number of siblings, goals scored)
Continuous: Any value in a range (e.g., height, temperature, time)

Statistical Displays

Different types of data call for different visual representations. Here are the key displays for Year 11 Mathematics:

Histogram

Used for continuous numerical data. Bars touch (no gaps) because the data is on a continuous scale. The x-axis shows class intervals and the y-axis shows frequency.

20-30: 3
30-40: 6
40-50: 9
50-60: 7
60-70: 4
70-80: 2

Example histogram showing frequency distribution (bars touch)

Box Plot (Box-and-Whisker)

Shows the five-number summary: minimum, Q1, median (Q2), Q3, and maximum. Great for comparing distributions and identifying skew.

MinQ1MedianQ3Max

Stem-and-Leaf Plot

Retains the original data values while showing the distribution shape. The stem is the leading digit(s) and the leaf is the final digit.

Stem| Leaf
2| 3 5 7
3| 1 2 4 6 8 9
4| 0 2 5 5 7 8 9
5| 1 3 6
6| 2 4

Key: 3|4 means 34

Choosing the Right Display

Categorical Bar chart, pie chart, frequency table
Discrete Dot plot, bar chart (with gaps), stem-and-leaf
Continuous Histogram (no gaps), box plot, cumulative frequency polygon
Comparing groups Back-to-back stem-and-leaf, parallel box plots

Key Vocabulary

Categorical Data

Data sorted into groups or categories. Can be nominal (no order) or ordinal (ordered).

Numerical Data

Data consisting of numbers that can be measured or counted. Can be discrete or continuous.

Five-Number Summary

Min, Q1, Median, Q3, Max. Used to construct a box plot.

Histogram

A display for continuous data using adjacent bars where bar area represents frequency.

Worked Examples

1

Classify each: (a) shoe size, (b) hair colour, (c) temperature, (d) satisfaction rating (1-5).

(a) Shoe size: Numerical discrete (countable sizes: 7, 7.5, 8, ...)

(b) Hair colour: Categorical nominal (no natural order)

(c) Temperature: Numerical continuous (any value in a range)

(d) Satisfaction rating: Categorical ordinal (ordered categories)

2

Data: 12, 15, 18, 22, 25, 28, 30, 35, 42, 48. Find the five-number summary.

Step 1: Data is already sorted. n = 10.

Step 2: Min = 12, Max = 48

Step 3: Median = (25 + 28)/2 = 26.5 (average of 5th and 6th values)

Step 4: Q1 = 18 (median of lower half: 12,15,18,22,25), Q3 = 35 (median of upper half: 28,30,35,42,48)

Answer: Five-number summary: 12, 18, 26.5, 35, 48

3

Create a stem-and-leaf plot for: 23, 31, 27, 45, 38, 42, 35, 29, 44, 36.

Step 1: Sort: 23, 27, 29, 31, 35, 36, 38, 42, 44, 45

Step 2: Stems are tens digits (2, 3, 4), leaves are units digits.

2 | 3 7 9

3 | 1 5 6 8

4 | 2 4 5

Key: 2|3 = 23

Knowledge Check

Select the correct answer for each question. Click "Check Answer" to see if you are right.

Question 1

What type of data is "number of pets in a household"?

Question 2

Which display is best for comparing the distributions of two groups?

Question 3

In a histogram, bars touch because:

Question 4

In a stem-and-leaf plot, 4|7 represents:

Question 5

A box plot shows Q1 = 20, Median = 30, Q3 = 45. What is the interquartile range (IQR)?

Key Concepts Summary

Year 11: Binomial Distribution Year 11: Central Tendency