Determining whether to use Inferential and Descriptive Statistics

Learning Module: Explanation

Welcome to this learning module!

In this module you will learn the difference between

Inferential and Descriptive statistics!

In later modules you will then determine when a question

should be answered with one or the other.

First, Descriptive statistics!

Simply put, descriptive statistics describe the features of a data set using numerical measures.

Simply put, descriptive statistics describe the features of a data set using numerical measures. And that’s it!

Simply put, descriptive statistics describe the features of a data set using numerical measures. And that’s it!Here’s an example

Meet Mrs. Graham,

a fifth Grade teacher having a parent teacher

conference.

The parent has some questions about her son

Bobby.

She will base her answers off of a class

data set.

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

She will base her answers off of a class

data set.

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

Data

She will base her answers off of a class

data set.

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

Data

Set

She will base her answers off of a class

data set.

Here are the parent’s questions with Mrs. Graham’s answers

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

What was Bobby’s score?

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

32

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

Out of how many

possible?

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

50

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

What were the highest and lowest

scores?

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

Highest 50,Lowest 31

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

What was the class average?

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

About 42

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

What was the most common

score?

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

45

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

Look’s like Bobby

needs more study time!

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

That’s probably a good idea.

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

Back to our definition:

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

descriptive statistics describe the features of a data set using

numerical measures

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

descriptive statistics describe the features of a data set using

numerical measures

Data Set

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

descriptive statistics describe the features of a data set using

numerical measures

Data Set

Numerical Measures

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

descriptive statistics describe the features of a data set using

numerical measures

Data Set

Numerical Measures

Highest to Lowest Score – THE RANGE

Most Common Score – THE MODE

Average Score – THE MEAN

Etc.

• While descriptive statistics focus on describing a data set,

• Inferential statistics aims to draw conclusions about a larger group (called a population),

• based on what is happening with a smaller group (called a sample).

• Inferential statistics studies a statistical sample, and from this analysis is able to say something about the population from which the sample came.

Now for Inferential statistics!

• While descriptive statistics focus on describing a data set,

• Inferential statistics aims to draw conclusions about a larger group (called a population),

• based on what is happening with a smaller group (called a sample).

• Inferential statistics studies a statistical sample, and from this analysis is able to say something about the population from which the sample came.

• While descriptive statistics focus on describing a data set,

• Inferential statistics aims to draw conclusions or INFER about a larger group (called a population),

• based on what is happening with a smaller group (called a sample).

• Inferential statistics studies a statistical sample, and from this analysis is able to say something about the population from which the sample came.

• While descriptive statistics focus on describing a data set,

• Inferential statistics aims to draw conclusions or INFER about a larger group (called a population),

• based on what is happening with a smaller group (called a sample).

• Inferential statistics studies a statistical sample, and from this analysis is able to say something about the population from which the sample came.

• While descriptive statistics focus on describing a data set,

• Inferential statistics aims to draw conclusions or INFER about a larger group (called a population),

• based on what is happening with a smaller group (called a sample).

• INFERential statistics studies a statistical sample, and from this analysis is able to say something about the population from which the sample came.

Same example, but here come a series of inferential questions

from the parent.

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

How does your class compare with other 5th grade classes: In the school?

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

About the same

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

What about other 5th

grade classes:

In the district?

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

A little better

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

What about other 5th

grade classes:

In the State

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

We are higher

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

What about other 5th

grade classes:

In the Country

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

We are much higher

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

Looks like your class does not represent

the national population

and is probably

doing better.

Maybe Bobby

doesn’t have to study as

much?

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

Maybe.

Mrs. Graham’s 5th Grade Class

Scores on Spelling Test

Bella 43

Betty 45

Bobby 32

Bonnie 45

Booker 38

Boston 45

Botania 50

Boyle 45

Bunder 31

A descriptive study examines the data from everyone in a group or population.A descriptive study cannot generalize to other like groups or populations.An inferential study examines the data from a sample and then generalizes the conclusions about that group to a larger population.

In summary -

A descriptive study examines the data from everyone in a group or population.A descriptive study cannot generalize to other like groups or populations.An inferential study examines the data from a sample and then generalizes the conclusions about that group to a larger population.

A descriptive study examines the data from everyone in a group or population.A descriptive study cannot generalize to other like groups or populations.An inferential study examines the data from a sample and then generalizes the conclusions about that group to a larger population.

A descriptive study examines the data from everyone in a group or population.A descriptive study cannot generalize to other like groups or populations.An inferential study examines the data from a sample and then generalizes the conclusions about that group to a larger population.

A descriptive study examines the data from everyone in a group or population.A descriptive study cannot generalize to other like groups or populations.An inferential study examines the data from a sample and then generalizes the conclusions about that group to a larger population.

Note – inferential and descriptive studies use the SAME statistics (e.g., mean, range, mode, etc.), but as you can see – for DIFFERENT reasons!