Meaning of Data

The word data simply means information that has been collected for a particular purpose. Data can be in the form of numbers, measurements, observations, or facts.

For example:

1. The ages of students in a class: 12, 13, 12, 14, 13


2. The number of cars sold each month


3. The names of favourite fruits among students

All these are examples of data.

When we collect data, they usually come in raw form — meaning they are not organized and may be difficult to understand at first.

Meaning of Data Presentation

Data presentation means arranging, organizing, and displaying data in a way that it can be easily read, understood, and interpreted.

When we present data properly, people can quickly see patterns, relationships, and differences between items.

For example: If you collect data on the number of students who like Mathematics, English, and Science, you can present it using a table, pictogram, bar chart, or pie chart.

Each of these methods helps to make the data clear and meaningful.

The main purpose of presenting data is to make it easier to understand and use.

Here are some reasons why we present data:

1. To make the data clear, organized, and meaningful.


2. To summarize large amounts of information in a simple form.


3. To help us compare different quantities or categories easily.


4. To allow us to see patterns or trends (e.g., increase or decrease over time).


5. To make it easier to analyze and interpret information.


6. To aid decision-making — for example, deciding which product sells best, or which subject most students like.


7. To make reports more attractive and easier to read, especially using charts and diagrams.

There are two main forms of data:

1. Qualitative Data

This refers to non-numerical data — things that describe qualities or categories.

Examples:

1. Colours of cars (red, blue, white)


2. Types of fruits (mango, orange, banana)


3. Names of students


4. Occupations (teacher, driver, doctor)

2. Quantitative Data

This refers to numerical data — data that can be counted or measured.

Examples:

1. Number of books in a library


2. Ages of students


3. Heights of students in centimetres

Quantitative data can further be divided into two types:

1. Discrete data: Can only take specific whole numbers (e.g., number of children in a family).


2. Continuous data: Can take any value within a range (e.g., weight, temperature, height).

When we collect data directly from observation, counting, or measurement, we usually get it in raw form — unarranged and unprocessed.

For example:

The marks scored by 10 students in a test are: 12, 14, 15, 10, 12, 8, 15, 9, 12, 13

This is raw data because it has not been arranged, summarized, or presented in a clear form. To understand it better, we need to organize and present it properly.

When you are asked to present data, follow these steps carefully:

1. Collect the data: Gather information through counting, measuring, survey, or research.


2. Record the data: Write down the raw data clearly without mistakes.


3. Organize the data: Arrange the data in order (ascending or descending) to make it easier to handle.


4. Group the data: If the data are many, you may group them into classes or intervals.


5. Summarize the data: Use tables, tallies, or charts to show the data more clearly.


6. Present the data: Display it in a suitable form such as a frequency table, pictogram, bar chart, or pie chart.


7. Interpret the data: Explain what the presentation means — for example, which is highest, lowest, or equal.

A well-presented data display should have these features:

1. It should be clear and easy to read.


2. It must have a title that explains what the data are about.


3. It must be neatly arranged with proper spacing and alignment.


4. It should include labels for rows, columns, or axes (where necessary).


5. If using diagrams or charts, there must be a key or legend explaining symbols used.


6. It should be accurate and not misleading.


7. It should make comparison easy between different values or categories.

There are several methods of presenting data, depending on the type of information and what you want to show. In Junior Secondary Mathematics, we commonly use the following:

1. Tables (especially Frequency Tables)


2. Pictograms (Picture Graphs)


3. Bar Charts / Bar Graphs


4. Pie Charts (Circle Graphs)


5. Line Graphs (for showing changes over time)

Each method will be explained in detail with examples.

Data presentation is not just for the classroom. It is used everywhere in life:

1. In business, to compare sales and profits.


2. In schools, to record and analyze students’ performance.


3. In government, to show population statistics or election results.


4. In science and research, to record experimental results.


5. In sports, to track scores and team performance.


6. In hospitals, to keep patient records and monitor health statistics.

It helps us to make informed decisions in every field.

Example of a Simple Data Presentation

A teacher asked 10 students how many pencils they each have. The answers are: 3, 5, 4, 5, 2, 3, 4, 3, 5, 4

That is raw data. We can present it as follows:

Number of Pencils	Frequency
2	1
3	3
4	3
5	3

Now we can easily see that:

1. The most common number of pencils is 3, 4, or 5 (each with frequency 3).


2. The smallest number is 2 (only 1 student).

This simple organization already helps us understand the data better.

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Meaning of Frequency Table

A frequency table is a way of organizing data to show how many times (frequency) each item or number occurs.

When we collect raw data, some values may appear more than once. By making a frequency table, we can count and record how often each value occurs.

It helps us to summarize the data clearly and quickly.

Meaning of Frequency

The frequency of an item means the number of times that item appears in a data set.

For example:

If the ages of 8 students are: 12, 13, 12, 14, 12, 13, 15, 12

1. The frequency of 12 is 4 (because 12 appears 4 times)


2. The frequency of 13 is 2


3. The frequency of 14 is 1


4. The frequency of 15 is 1

So, we can organize this information neatly in a frequency table.

Example 1: Simple Frequency Table (Without Grouping)

The marks scored by 10 students in a test are:
12, 14, 15, 10, 12, 8, 15, 9, 12, 13

Let’s make a frequency table.

Marks	Tally	Frequency
8	|	1
9	|	1
10	|	1
12	||||	4
13	|	1
14	|	1
15	||	2
Total		10

Explanation

We list each score under “Marks.”

For each score, we count how many times it appears and record it under “Frequency.”

We can use tally marks (||||) to make counting easier and to avoid mistakes.

The total frequency (sum of all frequencies) equals 10, which is the total number of students.

1. List the data (raw data).


2. Identify the smallest and largest values.


3. List all possible values between them (if data are few) or form class intervals (if data are many).


4. Make a tally column to count how many times each value occurs.


5. Count the tallies and record them in the frequency column.


6. Find the total frequency — this must equal the total number of items in the data.

We use a frequency table when:

1. The data are large or repeated.


2. We need to find patterns in data (like the most common value).


3. We want to prepare data for drawing graphs such as bar charts or histograms.


4. We want to find mean, median, or mode easily.

Grouped Frequency Table

When we have many different data values, listing them one by one may be too long. In that case, we group the data into class intervals (ranges).

Each interval covers a set of values (for example, 0–9, 10–19, 20–29, etc.). Then we count how many data items fall into each class.

Example 2: Grouped Frequency Table

The ages of 20 pupils in a class are:
10, 11, 13, 12, 14, 15, 13, 14, 10, 11, 15, 16, 12, 17, 15, 14, 13, 12, 14, 13

Let’s make a grouped frequency table using intervals of 10–12, 13–15, and 16–18.

Age Interval	Tally	Frequency
10 – 12	|||||	5
13 – 15	||||||	10
16 – 18	|||	3
Total		20

Explanation

The age intervals group the ages into 3 classes.

Each interval covers three values (e.g., 10–12 means 10, 11, and 12).

We count how many students’ ages fall into each group.

The total frequency adds up to 20 — same as the total number of pupils.

Class Interval Terms

In a grouped frequency table, each class interval has two limits:

1. Lower Class Limit: The smallest value in the class (e.g., 10 in 10–12).


2. Upper Class Limit: The largest value in the class (e.g., 12 in 10–12).


3. Class Size (or Class Width): The difference between consecutive lower limits. Example: If classes are 10–12, 13–15, 16–18, then class width = 3.

Example 3: Frequency Table with Class Width

The weights (in kg) of 15 students are:
35, 37, 39, 41, 42, 38, 37, 45, 47, 36, 39, 40, 44, 43, 42

Let’s use class width 5 to group them.

Weight (kg)	Tally	Frequency
35 – 39	|||||	5
40 – 44	|||||	5
45 – 49	|||	3
Total		15

Interpretation

The most common weight range (highest frequency) is 35–39 kg.

The least common range is 45–49 kg.

You can use this table to draw a bar chart or histogram later.

1. To summarize large data.


2. To see patterns (highest, lowest, most frequent values).


3. To prepare for statistical calculations such as mean, mode, median, and range.


4. To prepare for data presentation using charts.


5. To make comparisons easier.

1. It helps to reduce large data into manageable form.


2. It makes the data clear and easy to interpret.


3. It helps in identifying most or least frequent values quickly.


4. It is useful in constructing graphs (bar chart, histogram, etc.).


5. It can be used to calculate statistical measures easily.

Key Points to Remember

1. Always check that your total frequency equals the number of data items.


2. Decide whether the data need to be grouped or ungrouped.


3. Choose a class width that is neat and consistent.


4. Label your columns clearly: Class Interval, Tally, and Frequency.


5. Keep your table neat and easy to read.

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Meaning of a Pictogram

A pictogram (also called a pictograph) is a graphical way of presenting data using pictures or symbols to represent numbers.

Each picture or symbol represents a certain number of items, and the number of pictures tells us the quantity for each category.

It helps us to see and compare data quickly and easily.

Example of a Simple Pictogram

Suppose the following data show the number of cars sold by a company in four months:

Month	Number of Cars Sold	Pictogram
January	8	🚗🚗🚗🚗
February	12	🚗🚗🚗🚗🚗🚗
March	6	🚗🚗🚗
April	10	🚗🚗🚗🚗🚗

Key: 1 car symbol = 2 cars sold

Explanation

1. Each 🚗 stands for 2 cars.


2. For January: 4 car symbols × 2 = 8 cars


3. For February: 6 symbols × 2 = 12 cars


4. For March: 3 symbols × 2 = 6 cars


5. For April: 5 symbols × 2 = 10 cars

Steps for Drawing a Pictogram

1. Collect your data. Example: the number of fruits sold, number of students in each class, etc.


2. Choose a suitable symbol or picture. Example: 🍎 for apples, ⚽ for footballs, etc.


3. Decide the value of one symbol. Example: 1 symbol = 2 items, or ½ symbol = 1 item.


4. Draw the table with columns for the category and pictorial representation.


5. Draw the correct number of symbols for each category according to their values.


6. Include a key showing what each symbol stands for.

Example 2

A fruit seller recorded the number of fruits she sold in one week:

Fruit	Number Sold	Pictogram
Apples	10	🍎🍎🍎🍎🍎
Bananas	5	🍌🍌½🍌
Oranges	15	🍊🍊🍊🍊🍊🍊🍊½🍊
Mangoes	8	🥭🥭🥭🥭

Key: 1 symbol = 2 fruits

Explanation

1. Apples: 10 ÷ 2 = 5 symbols


2. Bananas: 5 ÷ 2 = 2½ symbols


3. Oranges: 15 ÷ 2 = 7½ symbols


4. Mangoes: 8 ÷ 2 = 4 symbols

The “½” symbol represents one fruit since half of 2 is 1.

Advantages of Using a Pictogram

1. It is simple and easy to understand.


2. It gives an attractive visual representation of data.


3. It is useful for comparing quantities quickly.


4. It helps younger learners or the general public to grasp information at a glance.


5. It helps in identifying trends easily (like which category is most or least).

Disadvantages of a Pictogram

1. It may not be suitable for large or very detailed data.


2. It can be difficult to draw half or quarter pictures accurately.


3. If the scale (value of symbol) is not chosen carefully, it may be misleading.


4. It is less accurate than numerical tables.

Important Notes

1. Always include a key or legend that explains what each symbol stands for.


2. Make sure the symbols are of equal size for all categories.


3. The pictures must be neatly aligned and easily countable.


4. If necessary, use half or quarter symbols to represent fractions.

Example 3 (Word Problem)

In a small farm, the number of animals are recorded as follows:

Goats: 12
Sheep: 8
Cows: 16
Chickens: 4

If 1 🐄 symbol represents 4 animals, draw a pictogram.

Animal	Number	Pictogram
Goats	12	🐐🐐🐐
Sheep	8	🐑🐑
Cows	16	🐄🐄🐄🐄
Chickens	4	🐓

Key: 1 symbol = 4 animals

Interpretation

1. Goats: 12 ÷ 4 = 3 symbols


2. Sheep: 8 ÷ 4 = 2 symbols


3. Cows: 16 ÷ 4 = 4 symbols


4. Chickens: 4 ÷ 4 = 1 symbol

From the pictogram, it is easy to see that the cows are the most numerous, while chickens are the least.

Uses of Pictograms

1. To represent small data sets in a simple visual way.


2. To make comparisons among categories easy.


3. To present data to non-technical audiences (like children or the public).


4. To make reports, posters, or charts more interesting and engaging.

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Meaning of a Bar Chart

A bar chart (or bar graph) is a graphical representation of data using bars or rectangles to show the quantity of each category.
The length or height of each bar represents the size or frequency of that category.

It helps us to compare quantities easily and see trends clearly.

1. It has bars (rectangles) of equal width but different heights.


2. The bars are separated by equal gaps to show that the data are discrete (not continuous).


3. The horizontal axis (x-axis) usually shows the categories or names.


4. The vertical axis (y-axis) shows the values or frequencies.


5. The height of each bar represents the value of the item.

1. Simple Bar Chart
   – Each category is represented by one bar only.
   – Used when we want to compare different items.


2. Multiple (or Compound) Bar Chart
   – Two or more bars are drawn side by side for each category.
   – Used to compare two or more related data sets, e.g. boys vs girls in classes.


3. Divided (or Component) Bar Chart
   – Each bar is divided into sections to show parts of a whole.
   – Used when total values are made up of components.

Example 1: Simple Bar Chart

The table below shows the number of books sold by a shop in one week:

Day	Number of Books Sold
Monday	30
Tuesday	45
Wednesday	25
Thursday	40
Friday	50

Steps to Draw the Bar Chart

1. Draw two perpendicular lines — the horizontal and vertical axes.


2. On the horizontal axis (x-axis), write the days.


3. On the vertical axis (y-axis), write the number of books sold (use a suitable scale, e.g. 1 cm = 10 books).


4. Draw bars for each day — bars must have equal width and equal spacing.


5. Label each bar and give your chart a title.

Diagram (Simple Bar Chart)

Number of Books Sold
│
│                         ██████
│                         ██████        Friday (50)
│                  ██████ ██████
│         ██████   ██████ ██████
│         ██████   ██████ ██████
│  ██████ ██████   ██████ ██████
│  ██████ ██████   ██████ ██████
│__________________________________________
   Mon     Tue     Wed     Thu     Fri

Interpretation

1. The highest bar (Friday) shows the most books were sold — 50.


2. The lowest bar (Wednesday) shows the fewest books were sold — 25.


3. The shop sold more books on Tuesday and Friday than on other days.

Example 2: Multiple Bar Chart

The table below shows the number of boys and girls in three classes.

Class	Boys	Girls
JSS 1	25	30
JSS 2	20	25
JSS 3	30	28

Steps to Draw

1. Draw two axes as before.


2. On the x-axis, write the classes (JSS 1, JSS 2, JSS 3).


3. On the y-axis, write the number of students.


4. For each class, draw two bars side by side — one for boys and one for girls.


5. Use different colors or shading for boys and girls.


6. Include a key or legend showing which color represents which group.

Diagram (Multiple Bar Chart)

Number of Students
│
│             ████ ██████
│             ████ ██████
│             ████ ██████
│      ████   ████ ██████
│      ████   ████ ██████
│      ████   ████ ██████
│________________________________
        JSS1   JSS2   JSS3

Legend:
████ = Boys
██████ = Girls

Interpretation

1. JSS 1 has more girls than boys.


2. JSS 2 also has more girls than boys.


3. JSS 3 has more boys than girls.

This chart helps us compare boys and girls across the three classes easily.

Example 3: Divided Bar Chart

A company’s monthly expenses are as follows:

Month	Rent	Salaries	Stationery	Total
January	10	25	15	50
February	12	30	18	60

Each total bar can be divided into parts for rent, salaries, and stationery.

Diagram (Divided Bar Chart)

Expenses
│
│         ██████████████████  Stationery
│         ██████████████████████████  Salaries
│         ████████████████████████████████  Rent
│__________________________________________
          January         February

1. Easy to read and interpret.


2. Shows comparisons clearly between different categories.


3. Visually appealing and simple to draw.


4. Suitable for both numerical and categorical data.


5. Can display trends or differences quickly.

1. Not suitable for continuous data (like temperature or time).


2. May become cluttered if too many bars are used.


3. Does not show exact values (unless labeled).


4. May mislead if scales are not chosen properly.

1. To represent discrete data such as number of students, items sold, or votes.


2. To compare different categories or groups.


3. To present survey results.


4. To summarize business or educational statistics.


5. To make visual comparisons in reports or lessons.

Key Points to Remember

1. All bars must have equal width and equal spacing.


2. The height of each bar must be proportional to its value.


3. Always label axes, include a title, and write units clearly.


4. Use a key or legend for multiple bar charts.

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Meaning of a Pie Chart

A pie chart (also called a circle graph) is a circular diagram divided into sectors.
Each sector represents a category of data, and its angle shows the proportion or percentage of that category compared to the whole.

Think of a pie chart like a round cake divided into slices — the bigger the slice, the larger the value it represents.

Features of a Pie Chart

1. The whole circle represents 360°, which stands for the total data.


2. Each category is represented by a sector (a portion of the circle).


3. The angle at the centre of each sector is proportional to its value.


4. All sectors together add up to 360°.


5. Used to show how parts make up a whole (percentages or fractions).

Formula to Find Each Sector Angle

Angle of a sector = ( Value of the item / Total of all values ) × 360°

Example 1: Drawing a Pie Chart

The table below shows how a student spends his day:

Activity	Hours
Sleeping	8
Studying	6
Playing	4
Eating	2
Others	4
Total	24

Step 1: Find the Sector Angles

Activity	Hours	Working	Angle
Sleeping	8	(8/24) × 360°	120°
Studying	6	(6/24) × 360°	90°
Playing	4	(4/24) × 360°	60°
Eating	2	(2/24) × 360°	30°
Others	4	(4/24) × 360°	60°
Total	24	—	360°

Step 2: Draw the Pie Chart

1. Draw a circle using your compass.


2. Draw a horizontal radius — this will be your starting line.


3. Use a protractor to measure the first angle (Sleeping = 120°) and draw the first sector.


4. From the new line, measure the next angle (Studying = 90°), and draw the next sector.


5. Continue until all the angles are drawn and the circle is complete.


6. Label each sector clearly and add different colors or shading for each activity.

Diagram of the Pie Chart

            _________
         .-'         '-.
       .'    Sleeping   '.
      /                   \
     ;       Studying       ;
     |        (90°)         |
     ;                     ;
      \      Playing (60°) /
       '.     Eating (30°).'
         '-. Others (60°)-'
            '-----------'

Step 3: Interpretation

1. The largest sector (Sleeping) shows most of the time (8 hours).


2. The smallest sector (Eating) shows the least time (2 hours).


3. The chart helps us see the daily routine clearly at a glance.

Example 2: Representing Class Results

The table shows the number of students who passed in different subjects:

Subject	Number of Students
English	40
Mathematics	50
Science	30
Social Studies	20
Yoruba	10
Total	150

Step 1: Find Each Sector Angle

Subject	Students	Calculation	Angle
English	40	(40/150) × 360°	96°
Mathematics	50	(50/150) × 360°	120°
Science	30	(30/150) × 360°	72°
Social Studies	20	(20/150) × 360°	48°
Yoruba	10	(10/150) × 360°	24°
Total	150	—	360°

Diagram of the Pie Chart

           _________
        .-'         '-.
      .' Mathematics    '.
     /                   \
    ;   English (96°)      ;
    |                      |
    ; Science (72°)        ;
     \ Social St. (48°)   /
      '.     Yoruba (24°).'
        '-.____________.-'

Step 3: Interpretation

1. The Mathematics sector is the biggest → Most students passed Mathematics.


2. The Yoruba sector is the smallest → Fewest students passed Yoruba.


3. The chart summarizes performance in a clear visual way.

Advantages of Pie Charts

1. They show the whole and its parts clearly.


2. Easy to understand and interpret.


3. Visually attractive — good for presentations and reports.


4. Good for percentage or proportion data.

Disadvantages of Pie Charts

1. Not suitable for large data sets.


2. Cannot show exact values easily.


3. Difficult to compare two or more pie charts.


4. Cannot show changes over time effectively.

Uses of Pie Charts

1. Showing how a budget is spent (e.g. salaries, transport, etc.).


2. Showing types of expenses in a business.


3. Representing student performance in different subjects.


4. Showing survey results in percentages.


5. Representing time allocation in a day or week.

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Meaning of Charts, Records, and Schedules

Charts,records, and schedules are ways of presenting information in an organized and visual form. They help us to understand, plan, and analyze data easily. They are commonly used in schools, offices, hospitals, and business organizations for keeping and interpreting information.

Charts

A chart is a visual representation of data using pictures, lines, or boxes to make information easier to read and compare. Charts summarize large data into a small space and give a quick understanding of relationships and trends.

Examples of Common Charts:

1. Bar Chart – shows comparison between different categories.


2. Pie Chart – shows parts of a whole using a circle divided into sectors.


3. Pictogram – uses pictures or symbols to represent data items.


4. Line Graph – shows changes over time by joining points with lines.


5. Histogram – used for continuous data (like age, time, or marks).

Example of a Simple Chart :

        BAR CHART: Number of Students in Each Class

      |          
   50 ┤            ████ JSS 3
   40 ┤       ████ JSS 2
   30 ┤  ████ JSS 1
      └─────────────────────
           JSS 1  JSS 2  JSS 3

Records

A record is a written or printed document that keeps information for reference or future use. Records are very important in schools, hospitals, offices, and businesses for keeping accurate data.

Examples of Records:

1. School attendance register


2. Student report card


3. Hospital patient record


4. Business sales record


5. Staff payroll record

Example of a School Attendance Record :

SCHOOL ATTENDANCE RECORD (WEEK 1)

+------------+--------+--------+--------+--------+--------+
| NAME       | MON    | TUE    | WED    | THU    | FRI    |
+------------+--------+--------+--------+--------+--------+
| Musa       | P      | P      | A      | P      | P      |
| Chika      | P      | P      | P      | P      | A      |
| Bayo       | A      | P      | P      | P      | P      |
+------------+--------+--------+--------+--------+--------+

Legend: P = Present, A = Absent

Schedules

A schedule is a table that shows planned activities, events, or duties arranged according to time, date, or order. Schedules help us to manage time and resources effectively.

Examples of Schedules:

1. Class timetable


2. Flight or train timetable


3. Work duty roster


4. Television or radio program guide

Example of a Class Timetable :

CLASS TIMETABLE (MONDAY)

+-----------+-----------+-----------+-----------+-----------+
| Time      | 8–9am     | 9–10am    | 10–11am   | 11–12pm   |
+-----------+-----------+-----------+-----------+-----------+
| Subject   | English   | Maths     | Break     | Science   |
+-----------+-----------+-----------+-----------+-----------+

Uses of Charts, Records, and Schedules

1. They help to organize data neatly.


2. They make information easy to read and understand.


3. They help in planning and decision-making.


4. They save time in presenting and retrieving information.


5. They help to track performance, attendance, or progress over time.

Differences Between Charts, Records, and Schedules

Aspect	Chart	Record	Schedule
Meaning	Visual representation of data	Written or printed information kept for reference	Plan or list of activities arranged by time
Purpose	To show comparison and relationship	To keep information for use	To plan or organize activities
Example	Bar chart, pie chart	Attendance register, sales record	Class timetable, duty roster

Advantages of Charts, Records, and Schedules

1. They present information clearly and attractively.


2. They help in analyzing and comparing data easily.


3. They help in planning and decision-making.


4. They reduce the chance of forgetting important events or data.

Disadvantages of Charts, Records, and Schedules

1. They may take time to prepare.


2. They require careful updating to remain accurate.


3. Charts may become confusing if too much data is used.