Teacher Guide: Statistical Measures

Learning Objectives 5-10 min lesson

Students will: Calculate and interpret mean, median, mode, and range for data sets; identify how outliers affect measures of center; and choose appropriate measures based on context.

Why this matters for FAST: Students must not only calculate these measures but also interpret them in context and understand when each measure is most appropriate.

Materials Needed

Whiteboard/projector
Student Concept Worksheet
Calculators
Number cards (optional)
Data set examples
Graph paper

Common Misconceptions to Address

Misconception #1: Mean and Median Are the Same

Students confuse mean (average) with median (middle value) or think they always give similar results.

How to Address:

"Mean is the AVERAGE - add all values and divide by how many. Median is the MIDDLE value when data is ordered. They can be very different, especially with outliers! Example: 1, 2, 3, 4, 100 has mean=22 but median=3."

Misconception #2: Forgetting to Order Data for Median

Students find the middle value without first putting data in order.

How to Address:

"ALWAYS order the data from least to greatest first! Then find the middle. If there are two middle numbers (even count), find their average."

Misconception #3: Mode Must Exist

Students think every data set must have exactly one mode.

How to Address:

"A data set can have NO mode (all values appear once), ONE mode, or MULTIPLE modes (bimodal, trimodal). If all values are different, there's no mode!"

Lesson Steps

1

Introduce the Four Measures (2 min)

MEAN: Add all values, divide by count (average)

MEDIAN: Middle value when ordered

MODE: Most frequent value

RANGE: Maximum minus minimum (spread)

2

Work Through an Example (2-3 min)

DATA SET:

Test scores: 85, 90, 78, 90, 92

Step 1 - Order: 78, 85, 90, 90, 92

Mean: (78+85+90+90+92)/5 = 435/5 = 87

Median: Middle value = 90 (3rd of 5)

Mode: 90 (appears twice)

Range: 92 - 78 = 14

3

Discuss Outliers (2 min)

SAY THIS:

"An OUTLIER is a value that is much higher or lower than the rest. Outliers affect the mean a LOT but don't change the median much. That's why we sometimes choose median over mean!"

Example: Add an outlier to our data: 78, 85, 90, 90, 92, 20

New mean: 455/6 = 75.8 (dropped a lot!)
New median: (85+90)/2 = 87.5 (barely changed)

4

When to Use Each Measure (2 min)

Use MEAN when: Data is evenly distributed, no extreme outliers

Use MEDIAN when: Data has outliers or is skewed (salaries, home prices)

Use MODE when: Finding most common/popular (shoe sizes, favorite color)

Use RANGE when: Showing spread or consistency

5

Guided Practice (2 min)

Ages of students in a club: 11, 12, 12, 13, 12, 14, 11

Order: 11, 11, 12, 12, 12, 13, 14
Mean: 85/7 = 12.1
Median: 12 (4th of 7)
Mode: 12 (appears 3 times)
Range: 14 - 11 = 3

Check for Understanding

Quick Exit Ticket:

Data: 10, 15, 20, 15, 100. Which measure of center best represents this data?

A) Mean (32) B) Median (15) C) Mode (15) D) Range (90)

Correct answer: B) Median (15) - The outlier (100) skews the mean too high. Median better represents the typical value.

IXL Skills to Assign

Recommended IXL Practice:

Calculate mean, median, mode, and range Interpret mean, median, mode, and range Changes in mean, median, mode, and range Identify an outlier Mean, median, and mode: which is best?

Differentiation & Extension

For struggling students: Use physical number cards students can arrange. Start with small data sets (5-7 values) with clear modes.

For advanced students: Challenge with finding a missing value given the mean. "The mean of 5 numbers is 10. Four numbers are 8, 9, 11, 12. What's the fifth?"

For home: Send Parent Activity sheet. Families can analyze sports statistics or household data.