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📖 Lesson 3 ⏱ ~30 min Year 10 · Unit 4 ⚡ +50 XP

Frequency Tables and Dot Plots

Organise data using frequency tables and display it with dot plots to identify patterns and outliers.

Today's hook:
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Core learning
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Worksheet

Worksheet

Use the worksheet to complete this lesson in your book or digitally.

Warm-up
Think First
+5 XP each

Q1 · How would you keep track of how many students in your class got each score on a spelling test?

Q2 · Imagine you rolled a die 30 times. How would you show which numbers came up most often in a way that is easy to read?

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From the lesson
Intentions

Learning Intentions

Know

  • A frequency table shows how often each value occurs. A dot plot displays each data point as a dot above a number line.

Understand

  • How the shape of a dot plot reveals the distribution, clusters, gaps and outliers in data.

Can Do

  • Create and interpret frequency tables and dot plots for small data sets.
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From the lesson
Key Terms

Key Terms

Frequency — The number of times a particular value occurs in a data set.
Dot plot — A display where each data value is shown as a dot above a number line.
Outlier — A data point that is significantly different from the other values.
Cluster — A group of data points that are close together on a display.
Gap — An interval with no data points between clusters.
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From the lesson
Misconceptions

Misconceptions to Fix

✗

Wrong: The tallest stack of dots in a dot plot is the mean.

✓

Right: The tallest stack is the mode (most frequent value). The mean requires calculation and may not correspond to any stack height.

✗

Wrong: Frequency tables must have equal class widths.

✓

Right: Frequency tables for individual (ungrouped) values do not use class widths at all. Class widths only apply when data is grouped into intervals.

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From the lesson
Content

Frequency Tables and Dot Plots

Work through the content, activities and worked examples below. Test your understanding with the questions in the Questions phase.

Remember Histogram bars touch because the horizontal axis represents continuous numerical data. Bar chart bars do not touch because the categories are separate.
Exam Tip When drawing a histogram, always label both axes and give the diagram a title. Use a ruler for straight edges.
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From the lesson
Activity
✏ Activity 1 — Draw a Histogram

Using the grouped frequency table from Activity 1 in Lesson 2:

  1. (a) Draw a histogram on graph paper.
  2. (b) Label the axes correctly.
  3. (c) Draw a frequency polygon on the same axes.
  4. (d) Describe the shape of the distribution (symmetric, skewed left, skewed right).
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From the lesson
Worked Example

Worked Example

Step-by-step
A survey records the heights (in cm) of 50 Year 10 students. Draw a histogram and frequency polygon for the data.
  1. 1
    Draw the axes: Vertical axis = Frequency, Horizontal axis = Height (cm).
  2. 2
    Draw the bars: For each class interval, draw a bar with height equal to the frequency. Bars must touch.
  3. 3
    Find midpoints: Calculate the midpoint of each class interval.
  4. 4
    Plot and join: Plot points at (midpoint, frequency) and join with straight lines to form the frequency polygon.
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From the lesson
Revisit

Revisit Your Thinking

Look back at your Think First response. What new understanding do you have now?

Reflect
Revisit your thinking
reflect

Earlier you were asked: What was your first thought on this topic?

Now that you've worked through the lesson, write a fuller answer. What changed in your thinking?

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From the lesson
Multiple Choice

Multiple Choice

Select the best answer for each question.

1 mark In a frequency table, the frequencies must always:

1 mark A dot plot is most useful for:

1 mark On a dot plot, a gap indicates:

1 mark An outlier on a dot plot appears as:

1 mark A frequency table for the data 3, 3, 4, 4, 4, 5, 5 shows frequency of 4 as:

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From the lesson
Short Answer

Short Answer

Show all working and justify your answers.

1. 4 marks The following grouped frequency table shows the masses (in kg) of 40 students:
50-59: 4, 60-69: 8, 70-79: 15, 80-89: 10, 90-99: 3.
(a) Draw a histogram for this data.
(b) On the same axes, draw a frequency polygon.
(c) Describe the shape of the distribution.

2. 3 marks Explain the difference between a histogram and a bar chart. In your answer, refer to the type of data each is used for and why the bars touch (or do not touch).

3. 2 marks A student claims that a frequency polygon can be drawn without first drawing a histogram. Is this true? Explain your answer.

Marking guidance: 1 mark each for MCQs. See mark allocations for each short answer question.

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