Frequency Histograms & Distributions Learning Objectives At - - PowerPoint PPT Presentation

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frequency histograms distributions learning objectives

Frequency Histograms & Distributions Learning Objectives At - - PowerPoint PPT Presentation

Mar 12, 2023 122 likes •438 views

Chapter 2.1 Frequency Histograms & Distributions Learning Objectives At the end of this lecture, the student should be able to: State the steps for drawing a frequency histogram. Name two types of distributions and explain how they

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Chapter 2.1

Frequency Histograms & Distributions

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SLIDE 2

Learning Objectives

At the end of this lecture, the student should be able to:

State the steps for drawing a frequency histogram.
Name two types of distributions and explain how they

look.

Define what an outlier is.
Say one reason why you would make a frequency

histogram.

Define relative frequency and cumulative frequency.

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SLIDE 3

Introduction

Review of frequency

histograms and relative frequency histograms

Description of five

common distributions in statistics

Explanation of outliers

Photo by BlairSmith66

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What is a Frequency Histogram?

Charting the Frequency Table

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SLIDE 5

Frequency Histogram

Explain what a

frequency histogram is

Describe the steps to

drawing a frequency histogram

Explain relative

frequency histogram

Photo by Rego Korosi

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SLIDE 6

What is a Frequency Histogram?

It’s a specific type of bar

chart made from data in a frequency table.

Frequency histograms

and relative frequency histograms.

The purpose of the chart

is to identify the “distribution” of the data.

Photo by Loqueveo

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SLIDE 7

Steps to Follow to Draw a Frequency Histogram

1. Make a frequency table.

Clas Class s Limit Limits Freq equenc uency Rela elativ tive Freq equenc uency 1-8 miles 14 0.23 9-16 miles 21 0.35 17-24 miles 11 0.18 25-32 miles 6 0.10 33-40 miles 4 0.07 41-48 miles 4 0.07 Total 60 1.00

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SLIDE 8

Steps to Follow to Draw a Frequency Histogram

1. Make a frequency table. 2. Draw a vertical line for the y- axis.

5 10 15 20 25 30 Frequency of Patients Class (Miles Transported)

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SLIDE 9

5 10 15 20 25 30 Frequency of Patients Class (Miles Transported)

Steps to Follow to Draw a Frequency Histogram

1. Make a frequency table. 2. Draw a vertical line for the y- axis. 3. Write “Frequency of _______” along the y-axis.

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SLIDE 10

5 10 15 20 25 30 Frequency of Patients Class (Miles Transported)

Steps to Follow to Draw a Frequency Histogram

1. Make a frequency table. 2. Draw a vertical line for the y- axis. 3. Write “Frequency of _______” along the y-axis. 4. Draw a horizontal line for the x-axis.

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SLIDE 11

5 10 15 20 25 30 Frequency of Patients Class (Miles Transported)

Steps to Follow to Draw a Frequency Histogram

1. Make a frequency table. 2. Draw a vertical line for the y- axis. 3. Write “Frequency of _______” along the y-axis. 4. Draw a horizontal line for the x-axis. 5. Write the classes below the x- axis and label them.

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SLIDE 12

5 10 15 20 25 30 Frequency of Patients Class (Miles Transported)

Steps to Follow to Draw a Frequency Histogram

6. For the first class, find the frequency in the table. Look for it on the y-axis and draw a horizontal line.

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SLIDE 13

5 10 15 20 25 30 Frequency of Patients Class (Miles Transported)

Steps to Follow to Draw a Frequency Histogram

6. For the first class, find the frequency in the table. Look for it on the y-axis and draw a horizontal line. 7. Draw two vertical lines down to make a bar.

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SLIDE 14

5 10 15 20 25 30 Frequency of Patients Class (Miles Transported)

Steps to Follow to Draw a Frequency Histogram

6. For the first class, find the frequency in the table. Look for it on the y-axis and draw a horizontal line. 7. Draw two vertical lines down to make a bar. 8. Repeat for all the other classes. 9. Color in the bars

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SLIDE 15

Relative Frequency Histogram

In the relative frequency

histogram, the relative frequency goes on the y- axis.

The chart looks takes on a

similar pattern.

Relative frequency better

for comparing two populations or two samples.

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Relative Frequency of Patients Class (Miles Transported)

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SLIDE 16

Frequency & Relative Frequency Histograms

After making a frequency

table, it is important to also make a frequency histogram and/or a relative frequency histogram.

These are used to reveal

the “distribution” in the data

Photo by Gabriel Miguel Gutierrez Valenzuela

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SLIDE 17

Understanding Distributions

Frequency Histograms Reveal Distributions

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SLIDE 18

Distributions

Define distribution and

why it is important to know the distribution

Describe outliers and

how they can be found using histograms

Example cumulative

frequency and ogives

Photo by Keith Hall from UK

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SLIDE 19

What is a Distribution?

It is the shape that is

made if you draw a line along the edges of a histogram’s bars.

A stem-and-leaf of the

same data will make the same shape on its side.

10 20 30 1-8 9-16 17-24 25-32 33-40 41-48 Frequency Class

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SLIDE 20

5 Main Types of Distributions

1. Normal distribution (also

called mound-shaped symmetrical)

2. Uniform distribution
3. Skewed left distribution
4. Skewed right distribution
5. Bimodal distribution

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SLIDE 21

5 Main Types of Distributions

1. Normal distribution (also

called mound-shaped symmetrical)

2. Uniform distribution
3. Skewed left distribution
4. Skewed right distribution
5. Bimodal distribution

1 2 3 4 5 6 7 1 2 3 4 5 6 Frequency Class

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SLIDE 22

5 Main Types of Distributions

1. Normal distribution (also

called mound-shaped symmetrical)

2. Uniform distribution
3. Skewed left distribution
4. Skewed right distribution
5. Bimodal distribution

1 2 3 4 5 6 7 1 2 3 4 5 6 Frequency Class

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SLIDE 23

5 Main Types of Distributions

1. Normal distribution (also

called mound-shaped symmetrical)

2. Uniform distribution
3. Skewed left distribution
4. Skewed right distribution
5. Bimodal distribution

1 2 3 4 5 6 7 1 2 3 4 5 6 Frequency Class

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SLIDE 24

5 Main Types of Distributions

1. Normal distribution (also

called mound-shaped symmetrical)

2. Uniform distribution
3. Skewed left distribution
4. Skewed right distribution
5. Bimodal distribution

1 2 3 4 5 6 7 1 2 3 4 5 6 Frequency Class

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SLIDE 25

5 Main Types of Distributions

1. Normal distribution (also

called mound-shaped symmetrical)

2. Uniform distribution
3. Skewed left distribution
4. Skewed right distribution
5. Bimodal distribution

1 2 3 4 5 6 7 1 2 3 4 5 6 Frequency Class

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SLIDE 26

Outliers

Outliers are data values that are “very different” from other measurements in the dataset.

2 4 6 Class 1 Class 2 Class 3 Class 4 Class 5 Class 6 Class 7 Class 8 Class 9 Frequency

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Cumulative Frequency

In “cumulative frequency”,

you add up all the classes before the class you are on.

The first class is always the

same as the frequency.

Each cumulative frequency

is equal to or higher than the last one.

Clas Class s Limit Limits Freq equenc uency

Cum Cumula ulativ tive e Frequ equenc ency

1-8 miles 14 14 9-16 miles 21 14+21=35 17-24 miles 11 35+11=46 25-32 miles 6 46+6=52 33-40 miles 4 52+4=56 41-48 miles 4 56+4=60 Total 60 60

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SLIDE 28

Chart of Cumulative Frequency: Ogive

Classes along the x axis,

and cumulative frequency along the y-axis

Because cumulative

frequency goes up from class to class, the ogive line always goes up to the top frequency.

From JLW87/Wikimedia Commons

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SLIDE 29

Distributions

There are 5 main types of

distributions used in statistics.

Histograms and stem-

and-leaf displays are used to look for outliers.

An ogive is a chart of

cumulative frequency.

Photo by Lariob

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SLIDE 30

Conclusion

The purpose of the

histogram is to reveal the distribution

Stem-and-leaf displays

also reveal the distribution

Knowing the distribution

is important in statistics

Photo by Mark Dixon