CH05-04 lesson

Measures of Spread Learning Activity

A focused Grade 6 learning session for Measures of Spread using visual models, worked examples, strategy guidance, and a short mastery check.

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15
minutes
6
lesson parts
11
practice items
Learning goal

Students will build Grade 6 mastery of measures of spread using models, equations, and test-style reasoning.

Student goal: I can solve problems involving measures of spread.

Helpful first: Mean and Median
concept

Learn the Idea

Measures of Spread means choosing a model, naming what each number means, and explaining the strategy.

  • Read the question carefully and identify what is being asked.
  • Choose a model, equation, table, or diagram that matches the situation.
  • Solve one step at a time and keep units or labels attached.
  • Use the answer explanation to check that the result makes sense.
visual model

See the Math

Visual Model 1

Question: The data set \(8, 12, 5, 19, 11, 6, 20\) is displayed on a number line. What is the range?

Visual Model 1

  • A. \(5\)
  • B. \(12\)
  • C. \(15\)
  • D. \(20\)

Why it works: Maximum is \(20\), minimum is \(5\). Range \(= 20 - 5 = 15\).

Answer: \(15\)

worked example

Follow a Worked Example

Example 1

Question: A box plot shows Q1 \(= 1.5\), median \(= 5\), and Q3 \(= 8.5\). What is the IQR?

Example 1

  • A. \(5\)
  • B. \(6.5\)
  • C. \(7\)
  • D. \(3.5\)
  1. IQR \(= Q3 - Q1 = 8.5 - 1.5 = 7\).

Answer: \(7\)

Example 2

Question: A box plot summary shows min \(= 2\), Q1 \(= 4.5\), median \(= 7.5\), Q3 \(= 10\), max \(= 14\). Find the range and IQR.

Example 2

  • A. Range \(= 12\), IQR \(= 5.5\)
  • B. Range \(= 12\), IQR \(= 3\)
  • C. Range \(= 7.5\), IQR \(= 5.5\)
  • D. Range \(= 5.5\), IQR \(= 2\)
  1. Range \(= \text{max} - \text{min} = 14 - 2 = 12\).
  2. IQR \(= Q3 - Q1 = 10 - 4.5 = 5.5\).

Answer: Range \(= 12\), IQR \(= 5.5\)

real world

Connect It to a Real Situation

Problem 1

Question: A farmer records the heights of \(6\) plants: \(12, 15, 13, 14, 16, 18\) inches. What is the range of the plant heights?

  • A. \(3\)
  • B. \(5\)
  • C. \(6\)
  • D. \(18\)

Why it works: Maximum \(= 18\), minimum \(= 12\). Range \(= 18 - 12 = 6\) inches.

Answer: \(6\) inches

strategy

Avoid Mistakes and Choose a Strategy

  • Rushing before identifying what the numbers represent.
  • Choosing an operation that does not match the situation.
  • Dropping labels, units, or context from the answer.
  • Skipping the estimate or reasonableness check.
  • Underline the question being asked.
  • Use a model before jumping to computation.
  • Write an equation that matches the story or picture.
  • Explain the final answer in a sentence.
summary

Remember the Key Idea

Measures of Spread becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.

GOLDEN RULE

Understand the model before choosing the operation.

Guided to independent practice

Solve before opening the answer

Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.

warmup

2 questions
G6-C05-T04-Q001 About 1 min

What is the range of the data set \(15, 22, 9, 30, 18\)?

  1. A \(21\)
  2. B \(18\)
  3. C \(9\)
  4. D \(30\)
Check answer and explanation

Answer A: \(21\)

Range \(=\) maximum \(-\) minimum \(=30-9=21\).

G6-C05-T04-Q002 About 1 min

The data set \(8, 12, 5, 19, 11, 6, 20\) is displayed on a number line. What is the range?

Measures of Spread visual for G6-C05-T04-Q002
  1. A \(5\)
  2. B \(12\)
  3. C \(15\)
  4. D \(20\)
Check answer and explanation

Answer C: \(15\)

Maximum is \(20\), minimum is \(5\). Range \(= 20 - 5 = 15\).

guided

1 question
G6-C05-T04-Q003 About 1 min

For the data set \(3, 7, 4, 9, 2, 8, 5\), arrange in order: \(2, 3, 4, 5, 7, 8, 9\). The median is \(5\) and the upper quartile is \(8\). What is the lower quartile?

  1. A \(2\)
  2. B \(5\)
  3. C \(4\)
  4. D \(3\)
Check answer and explanation

Answer D: \(3\)

The lower half of the ordered data is \(2, 3, 4\). The median of the lower half (lower quartile, Q1) is \(3\).

practice

5 questions
G6-C05-T04-Q004 About 1 min

A data set has minimum value \(12\), Q1 \(= 18\), median \(= 25\), Q3 \(= 32\), and maximum value \(40\). What is the interquartile range?

  1. A \(7\)
  2. B \(14\)
  3. C \(28\)
  4. D \(32\)
Check answer and explanation

Answer B: \(14\)

IQR \(= Q3 - Q1 = 32 - 18 = 14\). This measures the spread of the middle \(50\%\) of the data.

G6-C05-T04-Q005 About 1 min

Using the ordered data \(10, 14, 16, 22, 24, 26, 30, 35\), find Q1 and Q3, then compute the interquartile range.

  1. A \(6\)
  2. B \(12\)
  3. C \(13\)
  4. D \(25\)
Check answer and explanation

Answer C: \(13\)

Split the ordered data into two halves. The lower half is \(10,14,16,22\), so \(Q1=\frac{14+16}{2}=15\). The upper half is \(24,26,30,35\), so \(Q3=\frac{26+30}{2}=28\). The IQR is \(28-15=13\).

G6-C05-T04-Q006 About 1 min

A box plot of test scores shows Q1 \(= 72\), median \(= 80\), and Q3 \(= 88\). Which value represents the interquartile range?

  1. A \(8\)
  2. B \(16\)
  3. C \(20\)
  4. D \(88\)
Check answer and explanation

Answer B: \(16\)

IQR \(= Q3 - Q1 = 88 - 72 = 16\). The IQR tells us the spread of the middle half of the scores.

G6-C05-T04-Q007 About 1 min

Two data sets have the same mean of \(50\) but different spreads. Set A has a range of \(12\) and Set B has a range of \(30\). What does this tell you?

  1. A Set A has more variation than Set B.
  2. B The range cannot be compared between sets.
  3. C Both sets have identical variation.
  4. D Set B has more variation than Set A.
Check answer and explanation

Answer D: Set B has more variation than Set A.

A larger range indicates greater spread. Set B's range of \(30\) is larger than Set A's range of \(12\), so Set B has more variability.

G6-C05-T04-Q008 About 1 min

The mean absolute deviation (MAD) of a data set is the average distance of each data point from the mean. For the data \(5, 7, 9\), the mean is \(7\). The distances are \(|5-7| = 2\), \(|7-7| = 0\), \(|9-7| = 2\). What is the MAD?

  1. A \(0\)
  2. B \(\frac{4}{3}\)
  3. C \(2\)
  4. D \(4\)
Check answer and explanation

Answer B: \(\frac{4}{3}\)

MAD \(= \frac{2 + 0 + 2}{3} = \frac{4}{3} \approx 1.33\). The MAD shows how spread out the data is on average.

exit

3 questions
G6-C05-T04-Q009 About 1 min

For the data set \(2, 4, 6, 8\), the mean is \(5\). Calculate the MAD.

  1. A \(1\)
  2. B \(2\)
  3. C \(3\)
  4. D \(5\)
Check answer and explanation

Answer B: \(2\)

Distances: \(|2-5|=3\), \(|4-5|=1\), \(|6-5|=1\), \(|8-5|=3\). MAD \(= \frac{3+1+1+3}{4} = \frac{8}{4} = 2\).

G6-C05-T04-Q010 About 1 min

Which of the following statements about the range is true?

  1. A The range is always equal to the median.
  2. B The range is affected only by the mean.
  3. C The range only looks at the maximum and minimum values.
  4. D The range is found by adding the maximum and minimum.
Check answer and explanation

Answer C: The range only looks at the maximum and minimum values.

Range depends solely on the maximum and minimum, ignoring all middle values. It is found by subtracting the minimum from the maximum, not by adding them.

G6-C05-T04-Q011 About 1 min

A farmer records the heights of \(6\) plants: \(12, 15, 13, 14, 16, 18\) inches. What is the range of the plant heights?

  1. A \(3\)
  2. B \(5\)
  3. C \(6\)
  4. D \(18\)
Check answer and explanation

Answer C: \(6\)

Maximum \(= 18\), minimum \(= 12\). Range \(= 18 - 12 = 6\) inches.

Keep the learning path connected
Previous skillMean and Median Recommended nextDot Plots and Histograms Same strandStatistical Questions Same strandDescribing Data: Center, Spread, and Shape
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