The overall shape is easier to recognize in the:

chart.

---

Grouped Frequency Tables

Sometimes there are too many different values to list individually.

Consider test scores ranging from:

0 to 100.

Instead of listing every possible score, we could group them:

These ranges are called:

class intervals.

This produces a:

grouped frequency table.

---

Why Group Data?

Grouping can make a large dataset easier to:

summarize.

Instead of examining dozens of individual values, we can see how observations are distributed across:

ranges.

However, grouping also removes some detail.

If we know that seven students scored between 80 and 100, we do not know their exact scores from the grouped table.

So there is often a trade-off between:

detail and simplicity.

---

Choosing Intervals Carefully

Grouped intervals should:

• cover all possible values
• not overlap
• follow a logical order
• usually have consistent widths where appropriate

Poor intervals can make data difficult to:

interpret.

For example, these intervals are problematic:

0–10

10–20

because the value 10 appears to belong to:

both groups.

---

Scientific Data Tables

Tables are especially important in:

science.

Suppose a student investigates how temperature affects reaction time.

The headings include:

both the variable and its unit.

This is good scientific practice.

---

Independent and Dependent Variables

In experimental tables, the:

independent variable

is often placed in the first column.

The:

dependent variable

is usually placed in the next column or columns.

For the reaction example:

Independent variable → Temperature

Dependent variable → Reaction time

This arrangement makes the experimental relationship:

clear.

---

Repeated Measurements

Scientists often repeat measurements.

For example:

Repeated measurements allow scientists to:

• check consistency
• identify unusual measurements
• calculate averages
• improve reliability

Organizing repeated measurements carefully is essential for:

scientific analysis.

---

Accuracy in Data Presentation

A beautifully organized table is useless if the values are:

incorrect.

Always check:

• frequencies
• totals
• units
• headings
• scales
• transferred values
• calculations

A single transcription error can change the apparent:

pattern.

---

Misleading Charts

Charts can also be presented in ways that exaggerate or hide:

differences.

For example, consider:

Group A = 98

Group B = 100.

If a vertical axis begins at:

97

rather than zero, the difference may appear enormous.

The numerical difference is actually only:

2 units.

A graph is not automatically objective simply because it contains:

numbers.

---

Always Examine the Scale

When reading a chart, ask:

• Where does the axis begin?
• Are the intervals equal?
• Are the units clearly stated?
• Is anything missing?
• Does the visual appearance accurately represent the numerical difference?

Good data literacy means examining:

how information is presented, not just what numbers appear.

---

Worked Example 3: From Raw Data to Interpretation

Suppose 25 students record how many minutes they spend reading each evening:

20, 30, 20, 40, 10, 30, 20, 50, 30, 40, 20, 30, 10, 20, 40, 30, 20, 60, 30, 40, 20, 30, 50, 20, 30

Step 1: Identify the values

10, 20, 30, 40, 50, 60

Step 2: Count frequencies

Step 3: Check

2 + 8 + 8 + 4 + 2 + 1 = 25

Correct.

Step 4: Identify patterns

The most common reading times are:

20 and 30 minutes.

Only one student reported:

60 minutes.

Most students reported between:

20 and 40 minutes.

---

Asking Questions About Organized Data

Once data are organized, we can answer questions such as:

Which category has the greatest frequency?

Which has the smallest?

How many observations are there altogether?

Which values occur most often?

Are there any unusual values?

What overall pattern is visible?

These questions turn a table from a storage system into a tool for:

reasoning.

---

Data in Everyday Life

Organized data appear almost everywhere.

Examples include:

• weather reports
• sports statistics
• election results
• school grades
• financial reports
• fitness trackers
• transportation schedules
• product comparisons
• scientific research

Being able to organize and interpret data is therefore useful far beyond:

mathematics class.

---

Data in Science

Scientists collect enormous amounts of:

data.

Before they can interpret results, they must organize those data carefully.

For example:

Biology: population counts, heart rate, plant growth

Chemistry: temperature, concentration, reaction time

Physics: distance, velocity, force, energy

Environmental science: rainfall, pollution, biodiversity

Tables and charts help scientists identify:

relationships and patterns.

---

Data in Digital Tools

Spreadsheet programs can organize large datasets very efficiently.

They can:

• sort values
• count frequencies
• calculate totals
• calculate averages
• create charts
• filter categories
• identify patterns

However, software does not remove the need to understand:

what the data mean.

A computer can create a chart even when the chosen chart is:

inappropriate or misleading.

---

Choosing Between a Table and a Chart

Suppose you want someone to know that:

37 students chose Option A and 24 chose Option B.

A table communicates the exact numbers clearly.

If you want the audience to notice quickly that:

Option A was selected more often,

a bar chart may communicate the comparison more effectively.

The best format depends on:

what you want the reader to understand.

---

Communicating Data Effectively

Good data presentation should be:

Clear

The reader should understand what is being shown.

Accurate

The values must represent the original data correctly.

Complete

Important headings, labels, and units must be included.

Appropriate

The chosen table or chart should suit the type of data.

Readable

The information should not be unnecessarily complicated.

---

Common Mistake: Forgetting Units

Instead of:

Length

write:

Length (cm).

Instead of:

Time

write:

Time (s).

Instead of:

Mass

write:

Mass (g).

Units are part of the:

measurement.

Leaving them out makes scientific data incomplete.

---

Common Mistake: Incorrect Frequencies

Suppose the raw data contain:

2, 2, 3, 4, 2, 3.

The frequency of 2 is:

3

not 2.

Tally marks are useful because they reduce the chance of:

losing track while counting.

---

Common Mistake: Frequencies Do Not Match the Dataset

If there are:

30 observations,

the frequencies should add to:

30.

If they add to 29 or 31, something has probably been:

miscounted.

Always perform this simple:

total-frequency check.

---

Common Mistake: Mixing Data and Interpretation

Suppose a plant grew:

8 cm.

That is:

data.

Saying:

"The fertilizer caused the plant to grow faster"

is an:

interpretation.

The interpretation may or may not be supported by the experimental design.

Keep:

what was observed

separate from:

what you think it means.

---

Common Mistake: Choosing the Wrong Chart

Not every dataset should become a:

pie chart.

Not every dataset should become a:

line graph.

The representation should match:

the structure and purpose of the data.

Choosing a graph is part of:

data reasoning.

---

A Simple Data-Organization Process

When given raw data:

Step 1

Identify what each value represents.

Step 2

Check the units.

Step 3

Identify the different values or categories.

Step 4

Use tally marks if useful.

Step 5

Calculate the frequency of each value.

Step 6

Create a clearly labelled frequency table.

Step 7

Check that the frequencies total the number of observations.

Step 8

Choose an appropriate chart if a visual representation would help.

Step 9

Look for patterns.

Step 10

Describe those patterns accurately without making unsupported claims.

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Worked Example 4: Complete Data Organization

A class records the number of hours spent exercising during one week:

2, 4, 3, 5, 2, 3, 4, 3, 1, 2, 4, 5, 3, 2, 4, 3, 6, 2, 3, 4

Organize the data.

Frequency Table

Check:

1 + 5 + 6 + 5 + 2 + 1 = 20.

Correct.

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Displaying the Exercise Data