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What to create	Lesson plan
Which subject	Mathematics
What topic	Statistics
What length (min)	30
What age group	Year or Grade 11
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Year 11 Mathematics Lesson Plan: Introduction to Statistics

Lesson Duration

30 minutes

Learning Objectives

• Understand the basic concepts of statistics including mean, median, mode, and range.
• Collect and interpret data using statistical measures.
• Apply these measures to real-world scenarios.

Materials Needed

• Whiteboard and markers
• Graph paper
• Calculators
• Handouts with data sets

Lesson Outline

Introduction to Statistics (5 minutes)

Begin the lesson by asking students what they know about statistics.

• Discuss its importance in everyday life and various fields such as science, economics, and sports.
• Explain basic terminology: data, population, sample, and statistics.

Measures of Central Tendency (15 minutes)

1. Mean

   • Definition: The average of a set of numbers.
   • Formula: (\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}})

   [ \text{Example} : \text{Find the mean of the data set } [3, 7, 5, 10] ] [ \text{Mean} = \frac{3 + 7 + 5 + 10}{4} = \frac{25}{4} = 6.25 ]

2. Median

   • Definition: The middle value when data is ordered.
   • If there is an even number of observations, the median is the average of the two middle values.

   [ \text{Example} : \text{Find the median of the data set } [2, 3, 5, 9, 12] ]

   • Ordered: [2, 3, 5, 9, 12] => Median = 5

3. Mode

   • Definition: The number that appears most frequently in a data set.

   [ \text{Example} : \text{Find the mode of the data set } [4, 1, 2, 4, 3, 5, 3, 4] ]

   • Mode = 4

Measures of Dispersion (5 minutes)

1. Range

   • Definition: The difference between the highest and lowest values in a dataset.

   [ \text{Example} : \text{Find the range of the data set } [15, 20, 10, 30] ] [ \text{Range} = 30 - 10 = 20 ]

Class Activity (5 minutes)

• Split the class into small groups and give each group a dataset. Have them calculate the mean, median, mode, and range for their set.
• Each group will present their findings to the class.

Conclusion and Summary (5 minutes)

• Recap the definitions and formulas for mean, median, mode, and range.
• Discuss how these measures can influence decisions based on data.

Homework Assignment

1. For the following data set: [6, 7, 2, 8, 3, 6, 9, 6], calculate:

   • a) Mean
   • b) Median
   • c) Mode
   • d) Range

2. Create a scenario where determining the mean is more useful than the median, and explain why.

Homework Answers

1. Given the dataset: [6, 7, 2, 8, 3, 6, 9, 6]

   • a) Mean: [ \text{Mean} = \frac{6 + 7 + 2 + 8 + 3 + 6 + 9 + 6}{8} = \frac{47}{8} = 5.875 ]
   • b) Median: Ordered set: [2, 3, 6, 6, 6, 7, 8, 9] => Median = (\frac{6 + 6}{2} = 6)
   • c) Mode: 6
   • d) Range:
     [ \text{Range} = 9 - 2 = 7 ]

2. Scenario: Suppose you want to know the average score of students in a test. If the scores are highly skewed (for example, most students scored either very high or very low), the mean would be affected by the outliers more so than the median which is more representative of the actual central tendency of student performance. Therefore, using the median gives a better understanding of typical performance in such a case.

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This lesson plan aligns with the New Zealand Curriculum, encouraging critical thinking and collaborative learning among Year 11 students.