HistogramA frequency plot that shows the number of

times a response or range of responses occurred in a data set.

What is a histogram?

• A histogram is like a bar chart, but there are some important differences.

It can only be used to show continuous data The bars on a histogram touch. The bars

found on a bar graph do not touch.

It can only be used to show numerical data

The data is always grouped.

Histogram: Pros and Cons

Advantages:• Visually strong• Good for determining the shape of the data

Disadvantages:• Cannot read exact values because data is

grouped into categories • More difficult to compare two data sets

How do you make a histogram?

• Create a frequency table Count how many occurrences in the data– Be sure to create equal intervals

• Label the x and y axis– Choose a scale to label– X and Y axis do not need to have the same scale

• Draw a bar for each interval.– The height of the bar is the frequency for that interval. – Bars must touch but not overlap.

Let’s try!

A study collected the number of hours children watch TV. The collected the following number of hours: 8, 7, 5, 4, 9, 6, 3, 1, 7, 5, 4, 2, 3, 5, 2, 4, 3, 5, 7, 3, 6, 5, 3, 7, 2, 9, 6, 7, 8, 5, 4, 7, 3, 9, 4, 7, 3, 1, 2, 8, 5, 3, 7, 9, 5

1 6

2 7

3 8

4 9

5

Create the frequency table

Frequency Number of hours of TV

Number of hours of TV

6 1

7 2

8 3

9 4

5

Label x and y axis (Choose your scale!)Draw the bars

0

4

8

12

16

20

1-3 4-6 7-9

Analyzing HistogramsWhen you compare two or more data sets, focus on the following four features:

»Center»Spread»Shape»Unusual Features

How To Compare Distributions

To Find the Center:

5 6 7 8 9 10 11 12 13 14 15

List out the numbers in order, smallest to largest, then find the median.

Your Turn!

Spread (RANGE)

EXAMPLES

Less SpreadMore Spread

Highest – Lowest = Range

You Try!

3 Overall Shapes:• Normal/Symmetrical:

– The shape is symmetrical around the middle.

• Skewed left: – Most of the data is to the right, with a long

tail to the left.

• Skewed right: – Most of the data is to the left, with a long

tail to the right.

You Try!

Analyzing HistogramsUnusual Features

Unusual features refer to • gaps: areas of the distribution where there

are no observations and • Outliers: a data point that stands out from

the rest. (1.5 times the IQR)

EXAMPLES

Gap

Outlier

You Try!

Classwork/Homework

Graphical Displays for Data Homework