Statistical Diagrams

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Notes

Stem & Leaf Diagrams

A **stem-and-leaf diagram** displays an ordered list of data using digits; two-digit numbers split into tens (stem) and units (leaf).
Stem written vertically, leaves written horizontally in order; include a **key** showing how values are formed (e.g., 1|8 means 18).
To find the **median**, cross out numbers from ends until middle is reached; if two remain, find midpoint.
Common mistake: writing only the leaf (e.g., 6) instead of stem+leaf (e.g., 26) for median.

Bar Charts & Pictograms

A **bar chart** displays discrete data with bars of equal width separated by gaps; height shows frequency.
The **mode** is the outcome with the highest bar; dual bar charts compare two data sets side-by-side.
A **pictogram** uses symbols to represent frequency; a key shows value of one symbol (e.g., 1 shoe $= 2 students)$ .
Half or quarter symbols are used; to find median from bar chart, convert to table and use averages from tables method.

Pie Charts

A **pie chart** is a circle divided into sectors showing relative proportions; angles are proportional to frequencies.
To draw: find total frequency, calculate each sector angle as $(frequency/total) \times 360^{\circ}$ , then draw using protractor.
If chart says 'not to scale', use ratio/proportion; e.g., if $30^{\circ} = 15$ people, then $1^{\circ} = 0.5$ people.
Total frequency corresponds to 360°; sector angle $= (category$ frequency / total $frequency) \times 360^{\circ}$ .

Reading & Interpreting Statistical Diagrams

Read context, keys, axis labels, and units carefully; note any outliers or anomalies.
Describe trends using numbers from graph (e.g., 'temperature decreased from 12°C to 9°C').
Use exact wording from question; calculate mode, median, mean, or range to support explanations.
Consider limitations: small data set, bias, or scope (e.g., Jan-Mar data cannot predict August).

Comparing Statistical Diagrams

Compare trends (increases, decreases, peaks), steepness, and differences/similarities using numbers.
Calculate **mean** or **median** to compare averages; calculate **range** to compare spread.
Always relate calculations back to context; e.g., 'male range $= 5$ , female range $= 4$ , so males vary more'.
Be cautious: data may be unrepresentative (e.g., opening week of a shop) – state reasons.

Stem & Leaf Diagram Example

Bar Chart Example

Pie Chart Example

Dual Bar Chart Example

Practice questions

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1.In a stem-and-leaf diagram, the number 47 is represented as 4 | 7. What does the '4' represent?
Easy
- AThe tens digit
- BThe units digit
- CThe value 4
- DThe key
2.In a stem-and-leaf diagram, what is the purpose of the key?
Easy
- ATo show how to read the stem and leaves
- BTo unlock the diagram
- CTo indicate the total frequency
- DTo label the axes
3.A bar chart shows the favourite colours of students. The bar for 'Blue' is the tallest. Which average can be identified from this?
Easy
- AMode
- BMedian
- CMean
- DRange
4.In a pictogram, one symbol represents 4 people. How many symbols are needed to represent 10 people?
Easy
- A2.5
- B2
- C3
- D2.5 symbols
5.A pie chart shows the favourite sports of 40 students. The sector for football has an angle of 90°. How many students chose football?
Easy
- A10
- B20
- C15
- D12
6.The stem-and-leaf diagram shows the ages of 11 people. Key: 1|8 means 18 years. Stem: 1 | 8 9, 2 | 0 1 5 8 9, 3 | 5 6, 4 | 0. What is the median age?
Medium
- A25
- B26
- C28
- D29
7.The stem-and-leaf diagram shows blood pressure reductions (mmHg) for 11 patients. Key: 1|2 means 12 mmHg. Stem: 1 | 2 6 7 8 9, 2 | 1 3 4, 3 | 1 4, 4 | 0. What is the median reduction?
Medium
- A21
- B22
- C23
- D24
8.A dual bar chart compares the number of pets owned by Year 7 and Year 8 students. The Year 7 bar for 1 pet has height 10, and the Year 8 bar has height 8. How many more Year 7 students have 1 pet than Year 8?
Medium
- A2
- B18
- C10
- D8

Summary

## Statistical Diagrams - Quick Revision ### Stem & Leaf Diagrams - Split data into stem (tens) and leaf (units). E.g., 25 → 2 | 5. - Write stems vertically, leaves horizontally in order. - Include a **key** (e.g., 1|8 means 18). - **Median**: middle value; cross out from ends. If two middle, find midpoint. - **Mode**: most frequent leaf (or stem-leaf combo). ### Bar Charts & Pictograms - **Bar chart**: discrete data; bars separated, equal width; mode = highest bar. - **Pictogram**: uses symbols; key shows value per symbol (e.g., 1 shoe = 2 students). ### Pie Charts - Sector angle = (frequency / total) × 360°. - Angles proportional to frequencies; 360° = total frequency. - For problems: find value per 1° or per unit. ### Reading & Interpreting - Read titles, axes, keys, units. - Look for trends (increase, decrease, peak). - Use numbers from graph; write full sentences. - Consider if data is representative (e.g., small sample, bias). ### Comparing Diagrams - Compare averages (mean, median, mode) and spread (range). - Use numbers and context. - Comment on outliers and trends. **Key Formulas:** - Pie chart angle = (frequency / total) × 360° - Range = highest value - lowest value

Key terms

Stem-and-leaf diagram: A diagram that splits data into a stem (tens digit) and leaf (units digit) to show ordered data.
Key: Shows how digits in a stem-and-leaf diagram form values, including units.
Median: The middle value when data is ordered; for even number of values, it is the midpoint of the two middle values.
Mode: The value that occurs most frequently in a data set.
Bar chart: A chart with bars of equal width separated by gaps, used for discrete data; bar height shows frequency.
Pictogram: A chart using symbols to represent data; a key shows the value of one symbol.
Pie chart: A circle divided into sectors where each sector angle is proportional to the frequency of the category.
Sector angle: The angle of a sector in a pie chart, calculated as (frequency / total) × 360°.
Range: The difference between the highest and lowest values in a data set.

Slides

Stem & Leaf Diagrams

A stem-and-leaf diagram displays an ordered list of data using digits.
Two-digit numbers are split into a tens digit (stem) and a units digit (leaf).
The stem is written vertically, leaves are written horizontally in order.
A key explains how to read the digits $(e.g., 2|5 = 25)$ .

In a stem-and-leaf diagram, what does the stem represent?

The units digit
The tens digit
The frequency
The key

Finding the Median from a Stem-and-Leaf Diagram

The median is the middle value when data are ordered.
Cross out numbers from both ends until you meet in the middle.
If two numbers remain, find the midpoint between them.
Remember to include both stem and leaf when stating the median.

To find the median from a stem-and-leaf diagram, you must include both $the ____ and$ $the ____$ .

Bar Charts & Pictograms

A bar chart shows discrete data with bars of equal width separated by gaps.
The height of each bar represents the frequency.
A pictogram uses symbols to represent frequencies; a key shows the value of one symbol.
The mode is the outcome with the highest bar or most symbols.

In a bar chart, what does the height of a bar represent?

The category
The frequency
The mode
The range

Drawing Pie Charts

A pie chart is a circle divided into sectors showing proportions.
Each sector angle $= (frequency \div total) \times 360^{\circ}$ .
All angles must add up to 360°.
Draw a radius, then use a protractor to mark each angle.

To find the sector angle for a category, divide its frequency by $the ____ and$ multiply $by ____$ .

Solving Problems with Pie Charts

Angles are proportional to frequencies.
If a sector of 30° represents 15 people, then $1^{\circ} = 0.5$ people.
You can scale up: 360° gives the total frequency.
If the diagram says 'not to scale', use ratio and proportion, not a protractor.

A pie chart sector of 45° represents 20 people. How many people does 1° represent?

0.44
0.5
2.25
4

Reading & Interpreting Statistical Diagrams

Read titles, axes labels, and keys carefully.
Note the units (e.g., cm, thousands).
Look for trends: increases, decreases, peaks.
Use numbers from the diagram to support conclusions.

Which of these are true when interpreting statistical diagrams?

You should always check the key and units.
You can ignore the title if you understand the graph.
Trends should be described using numbers from the graph.

Comparing Statistical Diagrams

Compare trends, averages (mean, median, mode), and spread (range).
Use numbers from each data set in your comparisons.
Comment on differences and similarities.
Always relate calculations back to the context.

When comparing two data sets, which measure is best for comparing spread?

Mean
Median
Mode
Range

Common Mistakes & Tips

In stem-and-leaf, always include the key.
When finding median, write the full number (stem+leaf).
In bar charts, bars must have equal widths and gaps.
In pie charts, check all angles sum to 360°.

A common mistake in stem-and-leaf diagrams is to forget to include $the ____$ .

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