Teacher Guide: Data Displays

Learning Objectives 5-10 min lesson

Students will: Interpret and create histograms and box plots; identify key features including quartiles, median, and range; and describe the distribution and spread of data.

Why this matters for FAST: Students must read, interpret, and create data displays. They need to understand how the visual representation connects to statistical measures.

Materials Needed

Whiteboard/projector
Student Concept Worksheet
Graph paper
Rulers
Sample data sets
Colored pencils

Common Misconceptions to Address

Misconception #1: Histogram Bars Must Touch vs. Bar Graph

Students confuse histograms with bar graphs, not understanding that histogram bars touch because they show continuous data ranges.

How to Address:

"In a histogram, the bars touch because the data is continuous - one interval ends exactly where the next begins. Bar graphs show separate categories, so bars don't touch."

Misconception #2: The Box Plot Box Contains All Data

Students think all data points are inside the box, not realizing the box only contains the middle 50%.

How to Address:

"The box shows the middle 50% of data (from Q1 to Q3). The whiskers extend to the minimum and maximum, so ALL data is represented, but only the middle half is in the box!"

Misconception #3: Confusing Median Line with Mean

Students think the line inside the box plot shows the mean instead of the median.

How to Address:

"The line inside the box is ALWAYS the median - the middle value. It divides the data in half. The mean is not shown on a standard box plot!"

Lesson Steps

1

Introduce Histograms (2 min)

SAY THIS:

"A histogram shows how data is distributed across equal intervals. The height of each bar shows how many data points fall in that range. Unlike bar graphs, histogram bars TOUCH because the data is continuous."

Key features to identify:

Intervals (x-axis) - equal width ranges
Frequency (y-axis) - how many in each interval
Shape - symmetric, skewed left, skewed right
Gaps or clusters in the data

2

Introduce Box Plots (2-3 min)

SAY THIS:

"A box plot shows the five-number summary: minimum, Q1 (first quartile), median (Q2), Q3 (third quartile), and maximum. It lets us see the spread and identify if data is symmetric or skewed."

Five-Number Summary:

Minimum: Smallest value (left whisker end)
Q1: 25th percentile (left edge of box)
Median (Q2): 50th percentile (line in box)
Q3: 75th percentile (right edge of box)
Maximum: Largest value (right whisker end)
IQR: Q3 - Q1 (width of box)

3

Reading a Box Plot Example (2 min)

Example: Box plot showing test scores with Min=65, Q1=72, Median=80, Q3=88, Max=95

Range = 95 - 65 = 30
IQR = 88 - 72 = 16
Middle 50% scored between 72 and 88
Half the class scored above 80

4

Creating Displays from Data (2 min)

For Histograms: Choose intervals, count frequency for each, draw bars touching

For Box Plots: Order data, find five-number summary, draw box and whiskers

5

Choosing the Right Display (1 min)

Histogram: Best for showing shape of distribution
Box Plot: Best for showing spread and comparing groups

Check for Understanding

Quick Exit Ticket:

"In a box plot, if Q1 = 20 and Q3 = 50, what is the IQR?"

A) 70 B) 35 C) 30 D) 15

Correct answer: C) 30 (IQR = Q3 - Q1 = 50 - 20 = 30)

IXL Skills to Assign

Recommended IXL Practice:

Interpret histograms Create histograms Interpret box plots Create box plots Compare data displayed in box plots

Differentiation & Extension

For struggling students: Start with line plots (familiar from earlier grades). Use number cards to physically arrange data before drawing plots.

For advanced students: Compare two box plots to analyze different groups. Discuss how outliers would appear on box plots.

For home: Send Parent Activity sheet. Families can find data displays in newspapers, magazines, or online.