Student Concept Worksheet: Data Displays

What is a Histogram?

A histogram shows how data is distributed across equal intervals (ranges). It looks like a bar graph, but the bars TOUCH because the data is continuous.

Example: Test Scores of 20 Students

50-59 60-69 70-79 80-89 90-100

Score Ranges (intervals)

Key Features of Histograms:

Intervals (x-axis): Equal-width ranges (like 50-59, 60-69)
Frequency (y-axis): How many data points fall in each interval
Bars touch: Because data is continuous - one interval ends where the next begins
Shape: Can be symmetric, skewed left, or skewed right

What is a Box Plot?

A box plot (also called box-and-whisker plot) shows the five-number summary of data: minimum, Q1, median, Q3, and maximum.

The Five-Number Summary

MinimumSmallest value

Q125th percentile

Median (Q2)Middle value

Q375th percentile

MaximumLargest value

Example: Test Scores Box Plot

Min = 65, Q1 = 72, Median = 80, Q3 = 88, Max = 95

Min

Median

Max

Understanding the Box Plot:

The box contains the middle 50% of data (from Q1 to Q3)
The line inside the box is the median (NOT the mean!)
The whiskers extend to the minimum and maximum values
IQR (Interquartile Range) = Q3 - Q1 = width of the box

Feature	Histogram	Box Plot
Best for showing	Shape of distribution	Spread and center of data
Shows exact frequencies	Yes	No
Shows quartiles	No	Yes
Good for comparing groups	Harder to compare	Easy to compare side-by-side
Identifies outliers	Can see gaps	Can show as separate points

Guided Practice

Problem 1: Reading a Histogram

The histogram below shows the ages of people at a family reunion.

0-9 10-19 20-29 30-39 40-49

a) How many people are ages 10-19?

b) How many total people attended?

c) Which age range has the most people?

Problem 2: Finding the Five-Number Summary

Data set: 12, 15, 18, 20, 22, 25, 28, 30, 35

Minimum =

Q1 (median of lower half) =

Median (Q2) =

Q3 (median of upper half) =

Maximum =

IQR = Q3 - Q1 =

Problem 3: Reading a Box Plot

Use this box plot showing students' quiz scores:

a) What is the minimum score?

b) What is the median score?

c) What is the range?

d) What is the IQR?

e) What percent of students scored above 75?

Problem 4: Choosing the Right Display

For each situation, would a histogram or box plot be better? Explain why.

a) Comparing test scores between two classes:

b) Showing how many students fall into each grade range (A, B, C, D, F):

Data Displays