What is a Distribution?

We will illustrate what a distribution is with a data set that describes the hours students’ study

Here is the data set:

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Data

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Data Set

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

From this data set we will create a distribution:

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

The X Axis, will be the number of hours of

study

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

The Y Axis, indicates the number of times

the same number occurs

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

The Y Axis, indicates the number of times

the same number occurs

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

The Y Axis, indicates the number of times

the same number occurs

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

The Y Axis, indicates the number of times

the same number occurs

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

The Y Axis, indicates the number of times

the same number occurs

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

The Y Axis, indicates the number of times

the same number occurs

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Number of Occurrences

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Nu

mb

er

of

Occ

urr

en

ces

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Nu

mb

er

of

Occ

urr

en

ces

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Nu

mb

er

of

Occ

urr

en

ces

1

2

3

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Nu

mb

er

of

Occ

urr

en

ces

1

2

3

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Nu

mb

er

of

Occ

urr

en

ces

1

2

3

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Nu

mb

er

of

Occ

urr

en

ces

1

2

3

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Nu

mb

er

of

Occ

urr

en

ces

1

2

3

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Nu

mb

er

of

Occ

urr

en

ces

1

2

3

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Nu

mb

er

of

Occ

urr

en

ces

1

2

3

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Nu

mb

er

of

Occ

urr

en

ces

1

2

3

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Nu

mb

er

of

Occ

urr

en

ces

1

2

3

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Nu

mb

er

of

Occ

urr

en

ces

1

2

3

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Nu

mb

er

of

Occ

urr

en

ces

1

2

3

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Nu

mb

er

of

Occ

urr

en

ces

1

2

3

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Nu

mb

er

of

Occ

urr

en

ces

1

2

3

Student Hours of Study

Bart 1

Basheba 2

Bella 2

Bob 3

Boston 3

Bunter 3

Buxby 4

Bybee 4

Bwinda 5

Hours of Study1 2 3 4 5

Nu

mb

er

of

Occ

urr

en

ces

1

2

3

This is a distribution

One way to represent a distribution like this:

One way to represent a distribution like this:

One way to represent a distribution like this:

Is like this:

One way to represent a distribution like this:

Is like this:

One way to represent a distribution like this:

Is like this:Normal distributions have the majority of the data in

the middle

One way to represent a distribution like this:

Is like this:Normal distributions have the majority of the data in

the middle

One way to represent a distribution like this:

Is like this:

With decreasing but equal amounts

toward the tails

One way to represent a distribution like this:

Is like this:

With decreasing but equal amounts

toward the tails

With decreasing but equal amounts

toward the tails

Distributions can take other forms as well:

Distributions can take other forms as well:

Hours of Study

1 2 3 4# o

f O

ccu

rre

nce

s

7

Distributions can take other forms as well:

Distributions can take other forms as well:

Distributions can take other forms as well:

Distributions can take other forms as well:

Skewed RIGHT

Distributions can take other forms as well:

Hours of Study

5 6 72# o

f O

ccu

rre

nce

s1

Distributions can take other forms as well:

Skewed to the LEFT

Distributions can take other forms as well:

Distributions can take other forms as well:

Distributions can take other forms as well:

Or NON-NORMAL

Distributions can take other forms as well:

Distributions can take other forms as well: