Data Representation • Topic 3 of 3

Pie Charts, Line Graphs, and Stem-and-Leaf Plots

What is a Pie Chart?

A pie chart (or circle graph) is a circular chart divided into sectors (slices). Each sector represents a proportion of the whole data set. The entire circle represents 100% or the total frequency.

Calculating Pie Chart Angles:

Each sector's angle = $\frac{\text{Category Frequency}}{\text{Total Frequency}} \times 360^\circ$

What is a Line Graph?

A line graph shows data points connected by straight lines. It is ideal for showing trends over time or continuous change.

Features of Line Graph:

X-axis usually shows time (years, months, days)
Y-axis shows measured quantity
Points are plotted and connected
Multiple lines can compare different data sets

What is a Stem-and-Leaf Plot?

A stem-and-leaf plot is a way to organize data that shows both the shape of the distribution and the actual data values. The "stem" is the leading digit(s), and the "leaf" is the last digit.

Example: Data: 23, 25, 27, 31, 34, 35, 38, 42

Stem	Leaf
2	3, 5, 7
3	1, 4, 5, 8
4	2

Comparison of Graph Types:

Graph Type	Best Used For	Example
Pie Chart	Showing parts of a whole	Budget allocation
Line Graph	Showing trends over time	Temperature changes
Stem-and-Leaf	Displaying all data points concisely	Test scores

Solved Examples

Worked Example

In a survey of 40 people about their preferred mode of transport: Car: 16, Bus: 12, Bicycle: 8, Walk: 4. Draw a pie chart. Find the angle for each sector.

Solution

Step 1: Total = 16 + 12 + 8 + 4 = 40
Step 2: Car angle = (16/40) × 360° = 0.4 × 360° = 144°
Step 3: Bus angle = (12/40) × 360° = 0.3 × 360° = 108°
Step 4: Bicycle angle = (8/40) × 360° = 0.2 × 360° = 72°
Step 5: Walk angle = (4/40) × 360° = 0.1 × 360° = 36°
Step 6: Check sum: 144° + 108° + 72° + 36° = 360° ✓

Answer: Angles: Car=144°, Bus=108°, Bicycle=72°, Walk=36°

Worked Example

The temperature recorded at 6 AM each day for a week: Mon: 18°, Tue: 20°, Wed: 22°, Thu: 25°, Fri: 24°, Sat: 21°, Sun: 19°. Draw a line graph and find the day with highest temperature.

Solution

Step 1: Draw X-axis: Days (Mon to Sun)
Step 2: Draw Y-axis: Temperature (0° to 30°)
Step 3: Plot points: (Mon,18), (Tue,20), (Wed,22), (Thu,25), (Fri,24), (Sat,21), (Sun,19)
Step 4: Connect points in order with straight lines
Step 5: Add title: "Weekly Morning Temperature"
Step 6: Highest point is Thursday at 25°C

Answer: Line graph drawn. Highest temperature: Thursday (25°C).

Worked Example

Prepare a stem-and-leaf plot for the following test scores: 78, 85, 92, 67, 88, 74, 91, 83, 79, 86, 95, 81, 77, 84, 89, 73, 90, 82, 76, 80. Find the median.

Solution

Step 1: Sort the data: 67, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 88, 89, 90, 91, 92, 95
Step 2: Identify stems (tens digit): 6, 7, 8, 9
Step 3: Create plot:

Stem	Leaves
6	7
7	3, 4, 6, 7, 8, 9
8	0, 1, 2, 3, 4, 5, 6, 8, 9
9	0, 1, 2, 5

Step 4: Total 20 values, median is average of 10th and 11th values
Step 5: 10th value = 82, 11th value = 83
Step 6: Median = (82 + 83) ÷ 2 = 82.5

Answer: Stem-and-leaf plot created. Median = 82.5

Key Points

Pie chart: Circle divided into sectors; angle = (frequency/total) × 360°
Line graph: Points connected by lines; shows trends over time
Stem-and-leaf plot: Organizes data showing all values; stem = leading digit(s), leaf = last digit
Pie charts work best with 5-7 categories (too many slices become hard to read)
Line graphs are ideal for time series data
Stem-and-leaf plots preserve original data while showing distribution
Always sort leaves in ascending order for easier analysis

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.A pie chart shows parts of a:

Explanation: Parts of a whole.

Q2.The whole circle of a pie chart is:

Explanation: $360^\circ$.

Q3.A line graph best shows how data changes over:

Explanation: Over time.

Q4.A stem-and-leaf plot keeps the:

Explanation: Actual values.

Practice more MCQs → 📝 Assignment · 35 marks