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Lesson 5-2: Statistical Measures

Scenario: Test Scores Analysis - Calculate mean, median, mode, and range to analyze class performance!

Duration: 55-70 minutesScenario: Test Scores Analysis

Learning Objectives

  • Calculate the mean (average) of a data set
  • Find the median (middle value) of a data set
  • Identify the mode (most frequent value) in a data set
  • Calculate the range (difference between highest and lowest values)

Test Scores Analysis

Class Test Scores

A math teacher wants to analyze the performance of her class on a recent test. She collected the following scores out of 100 points:

Test Scores: 85, 92, 78, 96, 88, 85, 91, 89, 94, 87, 85, 90

85
92
78
96
88
85
91
89
94
87
85
90

Individual test scores

Step-by-Step Analysis

Step 1: Calculate the Mean (Average)

Mean = Sum of all scores ÷ Number of scores
Mean = (85+92+78+96+88+85+91+89+94+87+85+90) ÷ 12
Mean = 1060 ÷ 12 = 88.3

Step 2: Find the Median (Middle Value)

First, arrange in order: 78, 85, 85, 85, 87, 88, 89, 90, 91, 92, 94, 96
With 12 scores, median = average of 6th and 7th values
Median = (88 + 89) ÷ 2 = 88.5

Step 3: Identify the Mode (Most Frequent)

Count each score: 85 appears 3 times, others appear 1 time each
Mode = 85 (most frequent score)

Step 4: Calculate the Range

Range = Highest score - Lowest score
Range = 96 - 78 = 18

Summary: Mean = 88.3, Median = 88.5, Mode = 85, Range = 18

Statistical Measures

Mean (Average)

The sum of all values divided by the number of values.

Formula: Mean = Sum ÷ Count
Use: Shows the typical value

Median (Middle)

The middle value when data is arranged in order.

Method: Arrange in order, find middle
Use: Not affected by extreme values

Mode (Most Frequent)

The value that appears most often in the data set.

Method: Count frequency of each value
Use: Shows most common value

Range (Spread)

The difference between the highest and lowest values.

Formula: Range = Max - Min
Use: Shows how spread out the data is

When to Use Each Measure

Use Mean When:

  • • You want the typical value
  • • Data is fairly evenly distributed
  • • No extreme outliers
  • • Example: Average temperature

Use Median When:

  • • There are extreme values
  • • You want the middle value
  • • Data is skewed
  • • Example: House prices

Use Mode When:

  • • You want the most common value
  • • Data has clear peaks
  • • Categorical data
  • • Example: Favorite color

Use Range When:

  • • You want to know the spread
  • • Comparing variability
  • • Quick measure of dispersion
  • • Example: Test score spread

Practice Problems

Problem 1

Find the mean, median, mode, and range for these scores: 75, 80, 85, 90, 95, 80, 85

Your solution:

Problem 2

A student's test scores are: 88, 92, 85, 96, 88. Which measure (mean, median, or mode) would best represent their typical performance? Explain your choice.

Your reasoning:

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