Lesson 6-2: Statistical Measures

Master mean, median, and mode calculations with practical examples and real-world applications.

Statistics

Mean

Median

Mode

What You'll Learn

• Calculate the mean (average) of a data set
• Find the median (middle value) of a data set
• Identify the mode (most frequent value) in data
• Compare different statistical measures
• Choose the best measure for different situations

Mean (Average)

What is the Mean?

The mean is the average of all numbers in a data set. To find the mean, add all the numbers together and divide by how many numbers there are.

Formula:

Mean = Sum of all numbers ÷ Number of numbers

Example: Test Scores

Sarah's test scores: 85, 92, 78, 96, 89

Step 1: Add all scores: 85 + 92 + 78 + 96 + 89 = 440

Step 2: Count the scores: 5 scores

Step 3: Divide: 440 ÷ 5 = 88

Answer: Sarah's mean score is 88

When to Use the Mean:

When you want to know the typical value
When all numbers are important
When the data doesn't have extreme outliers
For calculating grades, temperatures, or prices

Practice Problem

Question: Find the mean of these numbers: 12, 15, 18, 21, 14

Your calculation:

Median

What is the Median?

The median is the middle number when data is arranged in order from smallest to largest. It's the number that splits the data in half.

Steps to Find the Median:

Arrange numbers from smallest to largest
Count the total number of values
If odd number of values: median is the middle number
If even number of values: median is the average of the two middle numbers

Example 1: Odd Number of Values

Heights (in cm): 120, 135, 142, 148, 155

Step 1: Numbers are already in order

Step 2: Count: 5 numbers (odd)

Step 3: Find middle: 142 cm

Answer: The median height is 142 cm

Example 2: Even Number of Values

Ages: 8, 10, 12, 14, 16, 18

Step 1: Numbers are already in order

Step 2: Count: 6 numbers (even)

Step 3: Two middle numbers: 12 and 14

Step 4: Average: (12 + 14) ÷ 2 = 13

Answer: The median age is 13

When to Use the Median:

When there are extreme values that might skew the mean
When you want to know the middle value
For income data, house prices, or test scores with outliers
When the data has a wide range

Practice Problem

Question: Find the median of these numbers: 7, 3, 9, 1, 5, 8, 2

Your calculation:

Mode

What is the Mode?

The mode is the number that appears most frequently in a data set. A data set can have one mode, multiple modes, or no mode at all.

Steps to Find the Mode:

Count how many times each number appears
Find the number that appears most often
If two or more numbers tie for most frequent, there are multiple modes
If all numbers appear the same number of times, there is no mode

Example 1: One Mode

Shoe sizes: 6, 7, 7, 8, 7, 9, 7, 8

• Size 6: appears 1 time

• Size 7: appears 4 times ← Most frequent

• Size 8: appears 2 times

• Size 9: appears 1 time

Answer: The mode is 7

Example 2: Multiple Modes

Test scores: 85, 90, 85, 88, 90, 87, 85, 90

• Score 85: appears 3 times

• Score 90: appears 3 times ← Both are most frequent

• Score 88: appears 1 time

• Score 87: appears 1 time

Answer: The modes are 85 and 90

When to Use the Mode:

When you want to know the most common value
For categorical data (colors, brands, types)
When looking for the most popular choice
For finding the most frequent score or measurement

Practice Problem

Question: Find the mode of these numbers: 2, 4, 2, 6, 4, 2, 8, 4

Your calculation:

Comparing Mean, Median, and Mode

Example: Test Scores

A class of 7 students scored: 85, 90, 78, 95, 88, 92, 85

Mean

(85+90+78+95+88+92+85) ÷ 7 = 87.3

Median

Ordered: 78, 85, 85, 88, 90, 92, 95

Middle value: 88

Mode

Most frequent: 85 (appears 2 times)

Use Mean When:

• Data is fairly balanced
• No extreme outliers
• Want the typical value
• All values are important

Use Median When:

• There are extreme values
• Data is skewed
• Want the middle value
• Outliers might mislead

Use Mode When:

• Looking for most common
• Categorical data
• Want popular choice
• Data has clear peaks

Practice Problems

Problem 1: Complete Analysis

Find the mean, median, and mode for these temperatures: 72°F, 75°F, 78°F, 72°F, 80°F, 72°F, 76°F

Mean:

Median:

Mode:

Problem 2: Choosing the Right Measure

A store owner wants to know the typical price of items sold. The prices are: $5, $8, $12, $15, $18, $20, $150

Which measure would be most useful and why?

Problem 3: Real-World Application

A teacher recorded the number of books each student read in a month: 3, 5, 2, 7, 4, 6, 2, 8, 3, 5, 2, 4

Questions:

What is the average number of books read?
What is the median number of books read?
What is the most common number of books read?
Which measure best represents the typical student's reading?

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