HistogramsBy Ryan Beil and Chris Carlson

Definition and Explanation

• A Histogram is a representation of a frequency distribution by means of rectangles whose widths represent class intervals and whose areas are proportional to the corresponding frequencies.

• Take the numbers: 1.2, 2.3, 2.5, 3.1, 3.5, 3.6, 3.7, 4.3, 4.5, 5.6, 6.7

1-1.991.2

2-2.99

2.3 2.5

3-3.99

3.1 3.5 3.6 3.7

4-4.99

4.3 4.5

5-5.995.6

6-6.996.7

Definition and Explanation Continued

1-1.99

2-2.99

3-3.99

4-4.99

5-5.99

6-6.99

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Occurance• Take the numbers:• 1.2, 2.3, 2.5, 3.1, 3.5, 3.6,

3.7, 4.3, 4.5, 5.6, 6.7

1-1.991.2

2-2.99

2.3

2.5

3-3.99

3.1

3.5

3.6

3.7

4-4.99

4.3

4.5

5-5.995.6

6-6.996.7

Definition and Explanation ContinuedA Histogram is a

representation of a

frequency distribution

by means of rectangles

whose widths represent

class intervals and whose

areas are proportional to

the corresponding

frequencies.

Frequency Distribution

Class Intervals

Rectangles/Widths

Proportional to Frequencies

Uses of Histograms• Histograms are used in many different ways and

forms.

1. United States Census2. Graphing Demographics

• Used when wanting to show a frequency of data for a specific interval or a group of intervals.

What is Needed to Make a Histogram?

• Intervals. (X Axis)• Frequencies for the intervals or interval groups.

(Y Axis)

• Example: Living With Parents (100 People Surveyed Per Age Group)

• 16-25: 60 People• 26-35: 40 People• 36-45: 20 People• 46-55: 15 People• 56-65: 5 People 16-25 26-35 36-45 46-55 56-65

0

25

50

75

100

Number of People Living With Their Parents

Age (Years)Nu

mb

er

of

Peop

le

Interval Frequency

How Long Does it Take Mrs.

Ellwood’s 4th Period Class to do

Homework?• Data:• 0-30 Minutes

o 4 People

• 31-60 Minuteso 8 People

• 61-90 Minuteso 3 People

• 91-120 Minuteso 2 People

• 121-150 Minuteso 0 People

• 151-180 Minuteso 3 People

0-30 31-60 61-90 91-120

121-150

151-180

0

2

4

6

8

10

How Long Does it Take Mrs. Ellwood’s 4th Period Class to

do Homework?

Minutes

Nu

mb

er

of

Stu

den

ts

Histogram QuestionA. Using the graph on the left,

find the median and the mode of the data. Provide your answer in interval form.

B. Five new students join Mrs. Ellwood’s class in the middle of the school year. Three chose the interval 121-150 and two chose the interval 61-90 for the amount of time spent on homework. Would this cause the median to change? If yes, then to what value?

0-30

31-60

61-90

91-120

121-

150

151-

180

0

4

8

How Long Does it Take Mrs. Ellwood’s 4th Period Class to

do Homework?

Minutes

Nu

mb

er

of

Stu

den

ts

Advantages• It displays a large range of data in a compact

area.

• Easy to compare data from different categories and intervals.

• Histograms can show bell curves. (Example Below)

Disadvantages• It can be more difficult to determine the exact

values for data and intervals.

• There is a restriction on the type of intervals and categories that can be used and compared.

• Can be difficult to read with a large number of intervals.

Bibliography • Images: (In Order of Appearance)

o http://phys.columbia.edu/~tutorial/estimation/gauss.png

o http://asq.org/learn-about-quality/data-collection-analysis-tools/overview/histogram2.html

o http://area.autodesk.com/userdata/fckdata/286966/image/nicolas/histogram_large.jpg

• Information:o http://quarknet.fnal.gov/toolkits/ati/histograms.html

o http://www.merriam-webster.com/dictionary/histogram

o http://asq.org/learn-about-quality/data-collection-analysis-tools/overview/histogram2.html

HistogramsDefinition and ExplanationDefinition and

Explanation ContinuedDefinition and Explanation Continued

Uses of HistogramsWhat is Needed to Make a Histogram?

How Long Does it Take Mrs. Ellwood’s 4th Period Class to do Homework

?Histogram QuestionAdvantagesDisadvantagesBibliography

Histograms