Statistical Diagrams

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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.

Bar chart: shoe sizes in class 11A

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) × 360°, then draw using protractor.
If chart says 'not to scale', use ratio/proportion; e.g., if 30° = 15 people, then 1° = 0.5 people.
Total frequency corresponds to 360°; sector angle = (category frequency / total frequency) × 360°.

Pie chart: favourite colours (30 students)

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).

Garden temperature at 7am each day

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.

Comparing books bought by male and female customers

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Übungsfragen

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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 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
7.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?
Easy
- A2
- B18
- C10
- D8
8.In a pie chart, the sector angle for a category is 72°. The total frequency is 60. What is the frequency of that category?
Easy
- A12
- B15
- C20
- D10

Mehr Fragen

9.A pie chart shows voters: women 240°, men 120°. 3360 more women voted than men. What is the total number of voters?
Hard
- A10080
- B5040
- C6720
- D8400
10.Two pie charts show ages in Adley and Bridford. The ratio of areas is the ratio of populations. If the radius of Adley's chart is 10 cm and Bridford's is 15 cm, what proportion of the total population lives in Adley?
Medium
- A0.307
- B0.400
- C0.444
- D0.308
11.A stem-and-leaf diagram shows heights of 20 men in cm. Key: 15|9 means 159 cm. Stem: 15 | 6 9, 16 | 4 5 7 8 9, 17 | 1 2 3 6 6 8 9, 18 | 0 2 3 8, 19 | 0 2. What percentage of men are taller than 184 cm?
Medium
- A15%
- B20%
- C25%
- D10%
12.A pie chart is drawn to show the birds seen: Magpie 15, Thrush 10, Starling 20, Sparrow 27. What is the sector angle for Sparrow?
Easy
- A108°
- B135°
- C120°
- D90°
13.A stem-and-leaf diagram shows test marks of 20 students. Key: 1|4 means 14 marks. Stem: 1 | 4 6 8 9, 2 | 1 2 3 5 7 9, 3 | 0 4 6 8 9, 4 | 1 3 6 6 8. One student is chosen at random. What is the probability their mark is less than 28?
Medium
- A0.5
- B0.45
- C0.55
- D0.6
14.In a stem-and-leaf diagram, the number 53 is represented as 5 | 3. What does the '5' represent?
Easy
- AThe tens digit
- BThe units digit
- CThe value 50
- DThe frequency
15.Two pie charts show ages in Adley and Bridford. The ratio of areas is the ratio of populations. If the radius of Adley's chart is 10 cm and Bridford's is 15 cm, what is the ratio of population of Adley to Bridford?
Medium
- A4:9
- B2:3
- C100:225
- D10:15
16.Two pie charts show the ages in two towns. The ratio of the number of people in Adley to Bridford is 4:9. In Adley, the sector for ages 0-19 is 90°. In Bridford, the sector for ages 0-19 is 60°. What proportion of the total population of both towns is aged 0-19? Give your answer correct to 3 significant figures.
Hard
- A0.192
- B0.154
- C0.231
- D0.212
17.The table shows how children travel to school: | Method | Walk | Car | Bicycle | Bus | |---|---|---|---|---| | Children | 12 | 7 | 9 | 4 | What is the sector angle for children who walk to school?
Easy
- A135°
- B120°
- C108°
- D144°
18.A stem-and-leaf diagram shows the ages of 11 people. Key: 1|8 means 18 years. Stem: 1 | 8 9, 2 | 0 1 3 5 8 9, 3 | 5 6, 4 | 0. What is the median age?
Medium
- A25
- B26
- C27
- D28
19.Two pie charts show ages in Adley and Bridford. The ratio of areas is the ratio of populations. If the radius of Adley's chart is 10 cm and Bridford's is 15 cm, and the total population of both towns is 13000, what is the population of Adley?
Medium
- A4000
- B5200
- C6000
- D8000
20.Two pie charts show the ages in two towns. The ratio of the number of people in Adley to Bridford is 4:9. In Adley, the sector for ages 0-19 is 90°. In Bridford, the sector for ages 0-19 is 120°. What percentage of the total population is aged 0-19?
Medium
- A30.8%
- B23.1%
- C20.0%
- D16.7%
21.In a stem-and-leaf diagram, what does the 'stem' represent?
Easy
- AThe tens digit of the data values
- BThe units digit of the data values
- CThe frequency of the data values
- DThe key of the diagram
22.A pictogram uses a symbol to represent 5 people. How many symbols are needed to represent 18 people?
Easy
- A3
- B3.6
- C4
- D2
23.In a bar chart, what does the height of each bar represent?
Easy
- AThe category
- BThe frequency
- CThe total number of data values
- DThe mode
24.A pie chart has a sector with an angle of 45°. The total frequency is 80. What is the frequency of that sector?
Easy
- A10
- B20
- C5
- D15
25.The stem-and-leaf diagram shows the ages of 12 people. Key: 1|2 means 12 years. Stem: 1 | 2 5 8 9, 2 | 0 1 3 6, 3 | 4 7, 4 | 0 2. How many people are aged 20 or older?
Easy
- A6
- B7
- C8
- D9
26.A dual bar chart compares the number of books read by boys and girls in a class. The bar for boys reading 5 books has height 6, and the bar for girls has height 9. How many more girls than boys read 5 books?
Easy
- A3
- B15
- C6
- D9
27.Two pie charts show the ages in two towns, X and Y. The radius of X's pie chart is 5 cm and Y's is 10 cm. The ratio of the number of people in X to Y is given by the ratio of the areas of the pie charts. What is the ratio of the number of people in X to Y?
Medium
- A1:4
- B1:2
- C2:1
- D1:1
28.A pie chart shows the favourite sports of 60 students. The sector for tennis has an angle of 60°. How many students chose tennis?
Easy
- A10
- B12
- C6
- D15
29.The stem-and-leaf diagram shows the heights of 13 plants in cm. Key: 2|3 means 23 cm. Stem: 2 | 3 5 8, 3 | 0 1 4 6 9, 4 | 2 5 7, 5 | 0 3. What is the median height?
Medium
- A36 cm
- B39 cm
- C35 cm
- D34 cm
30.In a bar chart, the bars should touch each other.
Easy
True or false?
31.A pie chart shows the favourite colours of 40 students. The sector for blue has an angle of 90°. How many students chose blue?
Easy
- A10
- B15
- C20
- D25
32.Match each statistical diagram to its correct description.
Medium
- Stem-and-leaf diagram
- Bar chart
- Pie chart
- Pictogram
- Shows data using digits
- Uses bars of equal width
- Circle divided into sectors
- Uses symbols to represent frequency
33.Which of the following are true about a stem-and-leaf diagram? (Select all that apply)
Medium
- AIt orders data from smallest to largest.
- BIt shows the frequency of each data value.
- CIt is used for continuous data only.
- DIt includes a key.
34.Arrange the steps for drawing a pie chart in the correct order.
Medium
- Calculate the angle for each category.
- Draw a circle and a radius to the top.
- Use a protractor to mark each sector.
- Label each sector and add a title.
35.The stem-and-leaf diagram shows the ages of 15 people. Key: 1|8 means 18 years. Stem: 1 | 2 4 5 8, 2 | 0 3 5 7 9, 3 | 1 4 6 8, 4 | 0 2. How many people are aged 30 or older?
Medium
- A4
- B5
- C6
- D7
36.A pictogram uses one symbol to represent 4 people. How many symbols are needed to represent 10 people?
Easy
37.Complete the sentence.
Easy
In a stem-and-leaf diagram, the key shows how to interpret the ____ and ____ digits.
38.In a bar chart showing the favourite sports of students, the bar for football is the tallest. Which average can be identified from this?
Easy
39.Explain why a pie chart is not suitable for showing how the temperature changes over a day.
Medium
40.A pictogram uses one symbol to represent 4 people. How many symbols are needed to represent 10 people?
Easy
- A3.5 symbols
- B2.5 symbols
- C1.5 symbols
- D4.5 symbols

Lernnotizen

## 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

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.

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