Meaning of Data

Definition:
Data means information or facts that are collected for a particular purpose.
It helps us to study and understand situations, make decisions, and solve problems.

For example:

1. The ages of pupils in a class.


2. The number of cars sold by a company each week.


3. The marks scored by students in a test.

Each piece of information is called a data item.

TYPES OF DATA

There are two main types of data:

1. Raw Data: Data that has just been collected and has not yet been arranged or organized.
   Example: 7, 12, 8, 6, 10, 7, 9, 8, 6


2. Grouped Data: Data that has been organized into classes or groups for easier analysis.
   Example: Ages of students grouped as 10–12, 13–15, 16–18, etc.

MEANING OF DATA PRESENTATION

Definition:
Data presentation means showing data or information in a way that is easy to read, understand, and interpret.

It helps us to see patterns, comparisons, and relationships clearly.

There are several ways of presenting data. These include:

1. Using Tables (Frequency Tables)


2. Using Bar Charts


3. Using Pie Charts


4. Using Pictograms


5. Using Line Graphs


6. Using Histograms

1. PRESENTATION USING TABLES (FREQUENCY TABLES)

Definition:
A frequency table is a table that shows how many times each value or group of values occurs in a given set of data.

Example 1:
The marks scored by 10 pupils are:
6, 8, 7, 9, 8, 6, 10, 7, 8, 9

Let us present them in a frequency table:

Marks	Tally	Frequency
6	||	2
7	||	2
8	|||	3
9	||	2
10	|	1
Total		10

Explanation:
The frequency shows how many times each mark appears in the data.
This makes it easy to count and compare.

2. PRESENTATION USING BAR CHARTS

Definition:
A bar chart is a diagram that uses rectangular bars to represent data.
The height or length of each bar shows the value or frequency of each item.

Example 2:
The number of fruits sold in a week is shown below:

Fruit	Number Sold
Orange	20
Banana	15
Mango	25
Apple	10

Text Diagram (Bar Chart):

Number Sold
|
|          ██████████████████████  (Mango)
|          ████████████████        (Orange)
|          ███████████             (Banana)
|          ██████                  (Apple)
|
|__________________________________________
   Apple   Banana   Orange   Mango

Explanation:
Each bar represents one type of fruit.
The tallest bar shows the most sold fruit.

3. PRESENTATION USING PIE CHARTS

Definition:
A pie chart is a circular chart divided into sectors (slices), where each sector represents a part of the whole data.
It helps us to see how each part compares to the total.

Example 3:
A student spends her day as follows:
Sleeping = 8 hours, Studying = 6 hours, Eating = 2 hours, Playing = 8 hours.

Total hours in a day = 24 hours

We find the angle for each activity:

Activity	Hours	Calculation	Angle
Sleeping	8	(8/24) × 360	120°
Studying	6	(6/24) × 360	90°
Eating	2	(2/24) × 360	30°
Playing	8	(8/24) × 360	120°
Total	24		360°

Text Diagram (Pie Chart):

           +-----------+
          /   Studying 90° \
         /                 \
   Playing 120°         Sleeping 120°
         \                 /
          \___ Eating 30°_/

Explanation:
The larger the angle, the greater the time spent on that activity.

4. PRESENTATION USING PICTOGRAMS

Definition:
A pictogram is a way of showing data using pictures or symbols.
Each picture stands for a certain number of items.

Example 4:
Number of books sold in 4 days:

Day	Books Sold	Symbol
Monday	10	📘📘
Tuesday	15	📘📘📘
Wednesday	20	📘📘📘📘
Thursday	5	📘

Explanation:
If one 📘 represents 5 books, then Tuesday (📘📘📘) means 15 books were sold.

5. PRESENTATION USING LINE GRAPHS

Definition:
A line graph is a diagram that uses lines to show how data changes over time.

Example 5:
Temperature of a town during five days:

Day	Temperature (°C)
Monday	25
Tuesday	28
Wednesday	30
Thursday	27
Friday	26

Text Diagram (Line Graph):

Temperature (°C)
|
|          * (30)
|        *     *
|      *         *
|    *             *
|___________________________
   Mon  Tue  Wed  Thu  Fri

Explanation:
We can see that the temperature increased up to Wednesday, then started to decrease.

6. PRESENTATION USING HISTOGRAMS

Definition:
A histogram is a special kind of bar chart used for continuous data (data grouped into intervals).
There are no gaps between the bars.

Example 6:
The ages of students in a class are grouped as follows:

Age Group	Frequency
10–12	4
13–15	6
16–18	8
19–21	2

Text Diagram (Histogram):

Frequency
|
|          ██████
|          ██████████
|          ██████████████
|          ████
|
|____________________________________
   10–12   13–15   16–18   19–21

Explanation:
Each bar represents an age group, and the height shows how many students fall into that group.

IMPORTANCE OF DATA PRESENTATION

1. It helps us to Understand information quickly.


2. It helps us to Compare data easily.


3. It helps us to Show trends, patterns, and relationships.


4. It helps us to Make decisions based on facts.


5. It helps us to Summarize large amounts of data clearly.

SUMMARY TABLE

Method	Tool Used	Best For
Table	Ruler, pencil	Listing data clearly
Bar Chart	Graph paper	Comparing quantities
Pie Chart	Protractor, compass	Showing proportions
Pictogram	Pictures or symbols	Showing simple data visually
Line Graph	Graph paper	Showing changes over time
Histogram	Graph paper	Showing continuous data

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MEANING OF PIE CHART

Definition:
A pie chart is a circular diagram that is divided into sectors (slices).
Each sector represents a part or category of the total data.
The whole circle represents the total or 100% of the data.

It helps us to compare different parts of data easily and to see which part is bigger or smaller.

Real-Life Example

Imagine a student’s day is divided into activities like this:

Activity	Time (hours)
Sleeping	8
Studying	6
Eating	2
Playing	8
Total	24

A pie chart helps us to show these activities as parts of a circle.

HOW TO DRAW A PIE CHART

To draw a pie chart, we use the following steps.

STEPS TO DRAW A PIE CHART

1. Step 1: Make a table showing all the data clearly.


2. Step 2: Find the total of all the data.


3. Step 3: For each category, calculate the angle for its sector using this formula:
   
   

   Formula: Angle for each sector = (Part ÷ Total) × 360°

   
   
4. Step 4: Use a protractor to draw the circle and measure each sector according to the angles.


5. Step 5: Label each sector clearly with its category and percentage.

EXAMPLE 1

The table below shows how a student spends 24 hours in a day:

Activity	Hours
Sleeping	8
Studying	6
Eating	2
Playing	8
Total	24

Step 1: Find the total hours = 24
Step 2: Find the angle for each activity.

Activity	Hours	Calculation	Angle
Sleeping	8	(8/24) × 360	120°
Studying	6	(6/24) × 360	90°
Eating	2	(2/24) × 360	30°
Playing	8	(8/24) × 360	120°
Total	24		360°

Step 3: Draw the pie chart.

               +-----------+
              /   Studying 90° \
             /                 \
   Playing 120°           Sleeping 120°
             \                 /
              \___ Eating 30°_/

Step 4: Label your chart

Sleeping – 120°

Studying – 90°

Eating – 30°

Playing – 120°

EXAMPLE 2

The table below shows how 200 students chose their favourite sport.

Sport	Number of Students
Football	80
Volleyball	50
Basketball	40
Tennis	30
Total	200

Step 1: Find total = 200
Step 2: Calculate angle for each sector.

Sport	Frequency	Calculation	Angle
Football	80	(80/200) × 360	144°
Volleyball	50	(50/200) × 360	90°
Basketball	40	(40/200) × 360	72°
Tennis	30	(30/200) × 360	54°
Total	200		360°

Step 3: Draw the circle and divide it according to the angles.

         +---------+
        / Football 144° \
       /                 \
  Tennis 54°          Volleyball 90°
       \                 /
        \___ Basketball 72°_/

EXAMPLE 3

The following table shows how a farmer uses his land.

Type of Crop	Area (Hectares)
Rice	40
Maize	30
Yam	20
Cocoa	10
Total	100

Step 1: Total = 100
Step 2: Find the angle for each crop.

Crop	Area	Calculation	Angle
Rice	40	(40/100) × 360	144°
Maize	30	(30/100) × 360	108°
Yam	20	(20/100) × 360	72°
Cocoa	10	(10/100) × 360	36°
Total	100		360°

Step 3: Draw the pie chart

          +----------+
         /  Rice 144° \
        /               \
   Cocoa 36°         Maize 108°
        \               /
         \____ Yam 72°_/

IMPORTANCE OF PIE CHARTS

It helps us to:

1. Show the relationship between parts and the whole clearly.


2. Compare different categories of data easily.


3. Present data in a simple and attractive way.


4. Understand percentages and proportions quickly.


5. Summarize large information visually.

ADVANTAGES OF PIE CHARTS

1. They are easy to read and understand.


2. They give a quick visual comparison of data.


3. They are suitable for showing percentage distribution.

DISADVANTAGES OF PIE CHARTS

1. They are not suitable for very large or complex data.


2. They cannot show changes over time.


3. They are not accurate for small differences between data values.

---

PRACTICE QUESTIONS (WITH STEP-BY-STEP SOLUTIONS)

Instructions: Show all working. Use Angle = (Part / Total) × 360° when drawing pie chart sectors. Use a protractor and ruler for drawing if required.

1. Question 1
   60 students were asked their favourite subject. The answers were: Mathematics 24, English 12, Science 10, Social Studies 8, Economics 6. Draw a pie chart showing the distribution. Show angle calculations and label each sector.
   
   Solution:
   
   1. Total = 24 + 12 + 10 + 8 + 6 = 60.
   
   
   2. Angle for Mathematics = (24 ÷ 60) × 360° = 0.4 × 360° = 144°.
   
   
   3. Angle for English = (12 ÷ 60) × 360° = 0.2 × 360° = 72°.
   
   
   4. Angle for Science = (10 ÷ 60) × 360° = 1/6 × 360° = 60°.
   
   
   5. Angle for Social Studies = (8 ÷ 60) × 360° = (2/15) × 360° = 48°.
   
   
   6. Angle for Economics = (6 ÷ 60) × 360° = 0.1 × 360° = 36°.
   
   
   7. Check: 144° + 72° + 60° + 48° + 36° = 360° (correct).
   
   

   Text diagram (approximate sector labels):
         +---------------------------+
        /   Mathematics 144°         \
       /                              \
      |  Social 48°       English 72°  |
      |                                |
       \      Science 60°  Economics 36°/
        \______________________________/
       

   Draw circle, place first ray at 0°, measure 144° for Mathematics, then continue adding sectors in order using protractor. Label each sector with subject and angle or percentage.



2. Question 2
   A farmer divides 180 hectares of farmland as follows: Maize 72 ha, Cassava 45 ha, Beans 27 ha, Vegetables 18 ha, Fallow 18 ha. Find the angle for each crop and state the largest crop by area.
   
   Solution:
   
   1. Total = 180 ha.
   
   
   2. Maize angle = (72 ÷ 180) × 360° = 0.4 × 360° = 144°.
   
   
   3. Cassava angle = (45 ÷ 180) × 360° = 0.25 × 360° = 90°.
   
   
   4. Beans angle = (27 ÷ 180) × 360° = 0.15 × 360° = 54°.
   
   
   5. Vegetables angle = (18 ÷ 180) × 360° = 0.1 × 360° = 36°.
   
   
   6. Fallow angle = (18 ÷ 180) × 360° = 36°.
   
   
   7. Largest by area = Maize (72 ha) corresponding to 144°.
   
   


3. Question 3
   A survey of 240 people asked what transport they use: Bus 96, Car 72, Bicycle 24, Walk 24, Others 24. Construct a pie chart; show percentage and angle for each category.
   
   Solution:
   
   1. Total = 240.
   
   
   2. Bus: percent = (96 ÷ 240) × 100% = 40%. Angle = 0.4 × 360° = 144°.
   
   
   3. Car: percent = (72 ÷ 240) × 100% = 30%. Angle = 0.3 × 360° = 108°.
   
   
   4. Bicycle: percent = (24 ÷ 240) × 100% = 10%. Angle = 36°.
   
   
   5. Walk: percent = 10%. Angle = 36°.
   
   
   6. Others: percent = 10%. Angle = 36°.
   
   
   7. Check percentages: 40% + 30% + 10% + 10% + 10% = 100%. Check angles: 144° + 108° + 36° + 36° + 36° = 360°.
   
   


4. Question 4
   In a class of 50 pupils the favourite colour choices are: Red 15, Blue 10, Green 8, Yellow 7, Black 5, White 5. Using the pie chart, find the angle representing Green. Also find the fraction of the circle for Red and simplify.
   
   Solution:
   
   1. Total = 50.
   
   
   2. Green angle = (8 ÷ 50) × 360° = (0.16) × 360° = 57.6°. If required to round to one decimal place: 57.6°.
   
   
   3. Red fraction = 15 ÷ 50 = 3 ÷ 10. Fraction of circle = 3/10 of 360° = 108°. Simplified fraction is 3/10.
   
   

   Interpretation: Green is about 57.6°, and Red takes 108° of the pie.



5. Question 5
   A student spends her pocket money on: Snacks 30%, Transport 25%, Savings 20%, School items 15%, Gifts 10%. Calculate angle for Snacks and for Savings. Then sketch a labelled pie-chart text diagram.
   
   Solution:
   
   1. Angle for Snacks = 30% of 360° = 0.30 × 360° = 108°.
   
   
   2. Angle for Savings = 20% of 360° = 72°.
   
   
   3. Other angles: Transport 25% → 90°; School items 15% → 54°; Gifts 10% → 36°.
   
   

   Text diagram (labelled sectors):
      +---------------------------+
     /   Snacks 108°   Transport90° \
    |                                 |
    |  Savings72°        School54°     |
     \        Gifts36°               /
      \_____________________________/
       



6. Question 6
   In a survey 300 people rated service as Excellent 90, Good 120, Fair 60, Poor 30. A pupil forgot the total and used 250 as total when computing angles. Explain the error and compute the correct angles. Show also what wrong angles the pupil would have obtained using 250.
   
   Solution:
   
   1. Correct total = 90 + 120 + 60 + 30 = 300.
   
   
   2. Correct angles: Excellent = (90 ÷ 300) × 360° = 108°; Good = (120 ÷ 300) × 360° = 144°; Fair = (60 ÷ 300) × 360° = 72°; Poor = (30 ÷ 300) × 360° = 36°.
   
   
   3. Pupil used wrong total 250. Wrong angles would be: Excellent = (90 ÷ 250) × 360° = 129.6°; Good = (120 ÷ 250) × 360° = 172.8°; Fair = (60 ÷ 250) × 360° = 86.4°; Poor = (30 ÷ 250) × 360° = 43.2°. These sum to 432° due to inconsistent scaling (in fact they still sum to 360° because each percentage is scaled but relative proportions differ; check: 129.6 +172.8 +86.4 +43.2 = 432° — this reveals the pupil misapplied because proportions were larger; the real issue is that using wrong total gives incorrect relative sizes and will not represent the true data fractions).
   
   
   4. Conclusion: Always use correct total. Using 250 distorts the chart and misleads interpretation.
   
   


7. Question 7
   The marks of 40 students in a short test are grouped as: 0–9 (4), 10–19 (6), 20–29 (10), 30–39 (12), 40–49 (8). Use the grouped frequencies to make a pie chart by first converting each class frequency to angle. Give angles for each class.
   
   Solution:
   
   1. Total frequency = 4 + 6 + 10 + 12 + 8 = 40.
   
   
   2. Angles: 0–9: (4 ÷ 40) × 360° = 36°.
   
   
   3. 10–19: (6 ÷ 40) × 360° = 54°.
   
   
   4. 20–29: (10 ÷ 40) × 360° = 90°.
   
   
   5. 30–39: (12 ÷ 40) × 360° = 108°.
   
   
   6. 40–49: (8 ÷ 40) × 360° = 72°.
   
   
   7. Check: 36 + 54 + 90 + 108 + 72 = 360°.
   
   


8. Question 8
   A company reports sales by region: North 22%, South 28%, East 18%, West 20%, Central 12%. One trainee draws the sector for North as 80°. Check the trainee work and compute correct sector sizes. State the error in degrees made by the trainee for North.
   
   Solution:
   
   1. Correct North angle = 22% of 360° = 0.22 × 360° = 79.2°.
   
   
   2. Trainee used 80°. Error = 80° − 79.2° = 0.8° too large.
   
   
   3. Other correct angles: South = 0.28 × 360° = 100.8°; East = 0.18 × 360° = 64.8°; West = 0.20 × 360° = 72°; Central = 0.12 × 360° = 43.2°.
   
   
   4. Check sum: 79.2 + 100.8 + 64.8 + 72 + 43.2 = 360°.
   
   

   Interpretation: The trainee rounding to 80° is acceptable in practical drawing but note rounding error of 0.8°.



9. Question 9
   A pupil collected data on daily water usage (litres) in a household: Bath 120, Cooking 30, Washing 50, Cleaning 20, Drinking 10. Create a pie chart by calculating the angle for Bath and the percentage share for Washing. Show working.
   
   Solution:
   
   1. Total usage = 120 + 30 + 50 + 20 + 10 = 230 litres.
   
   
   2. Bath angle = (120 ÷ 230) × 360° = (120 × 360) ÷ 230 = 43,200 ÷ 230 ≈ 187.8261° ≈ 187.83° (to two decimals).
   
   
   3. Washing percentage = (50 ÷ 230) × 100% ≈ 21.7391% ≈ 21.74% (to two decimals).
   
   
   4. Optional: Washing angle = 0.217391 × 360° ≈ 78.26°.
   
   
   5. Check: approximate angles sum ≈ 187.83 + 46.96 + 78.26 + 31.30 + 15.65 ≈ 360° (small rounding differences allowed).
   
   

   Interpretation: Bath uses the largest share of water about 52.17% (120/230), accounting for about 187.83° of pie.



10. Question 10
    A pie chart of election votes shows Party A 126°, Party B 90°, Party C 72°, Party D 36°. If total registered votes counted were 10,000, find the number of votes each party obtained. Show full working.
    
    Solution:
    
    1. Total angle = 360° corresponds to 10,000 votes. So 1° corresponds to 10,000 ÷ 360 ≈ 27.777... votes.
    
    
    2. Party A votes ≈ 126 × (10,000 ÷ 360) = 126 × 27.777... ≈ 3,500.
    
    
    3. Party B votes ≈ 90 × 27.777... = 2,500.
    
    
    4. Party C votes ≈ 72 × 27.777... = 2,000.
    
    
    5. Party D votes ≈ 36 × 27.777... = 1,000.
    
    
    6. Check sum: 3,500 + 2,500 + 2,000 + 1,000 = 9,000. Wait this is 9,000; recheck conversion: 360° → 10,000, 1° = 10,000/360 ≈ 27.777..., multiply: 126×27.777... = 3,500 correct; 90×27.777... = 2,500; 72×27.777... = 2,000; 36×27.777... = 1,000. Sum = 9,000. The missing 1,000 indicates that the given angles sum to 324°, not 360°. Compute sum of given angles: 126 + 90 + 72 + 36 = 324°. Therefore the pie chart is incomplete or some category missing with 36° (or the total votes correspond to 324°). If total is 10,000 and angles sum to 324°, then scale factor is 10,000 ÷ 324 ≈ 30.8642 votes per degree. Then real votes: Party A = 126 × 30.8642 ≈ 3,888; Party B = 90 × 30.8642 ≈ 2,777; Party C = 72 × 30.8642 ≈ 2,222; Party D = 36 × 30.8642 ≈ 1,111; Sum ≈ 10,000.
    
    
    7. Conclusion: Either pie chart omitted a category of 36° or supplied angles do not sum to 360°. Point out the inconsistency and show corrected distribution as above.
    
    

SUMMARY TABLE

Concept	Description
Definition	A circular diagram showing data as sectors.
Formula	Angle = (Part / Total) × 360°
Use	To compare parts of a whole (percentages, categories).
Tool	Compass, ruler, protractor, pencil.
Best for	Showing proportion or percentage data.