A frequency plot that shows the number of times a response or range of responses occurred in a data set.

HISTOGRAM

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

WHAT IS A HISTOGRAM?

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.

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

HISTOGRAM: PROS AND CONS

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.

HOW DO YOU MAKE A HISTOGRAM?

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

Number of hours of TV

III 6 II 1

IIII IIII 7 IIII 2

III 8 IIII IIII 3

IIII 9 IIII I 4

IIII III 5

Frequency Number of hours of TV

14 1-3

16 4-6

15 7-9

LABEL X AND Y AXIS (CHOOSE YOUR SCALE!)DRAW THE BARS

0

4

8

12

16

20

1-3 4-6 7-9

How To Compare Distributions

Analyzing Histograms and Dot Plots

Analyzing Histograms

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

»Center»Spread»Shape»Unusual Features

Analyzing Histograms and Dot Plots

Center (It is the MEDIAN)!

EXAM

PLE

5 6 7 8 9 10 11 12 13 14 15

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.

6,6,6,7,8,8,8,9,10,10,10,10,10,11,12Center

Your Turn!

Analyzing Histograms and Dot Plots

Spread (RANGE)

EXAMPLES

Less Spread

4

More Spread

8

Highest – Lowest = Range

You Try!

Analyzing Histograms and Dot Plots

Shape

The shape of a distribution is described by symmetry, amount of skew, number of peaks, etc.

EXAM

PLE

S

Symmetric, Unimodal

Skewed Left

Skewed Right

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