Intro Stats

Lesson 2.1 A

Objective: SSBAT construct a frequency distribution.

Standards: S2.5B

A Limited Lunch

At lunch, twelve of the children chose from the following types of sandwiches: peanut butter, jelly, peanut butter and jelly, marshmallow fluff, jelly and fluff, or peanut butter and fluff. Oliver does not like nuts and so chose to have just a jelly sandwich, as

did Kenny. Kate had plain peanut butter on her sandwich and so did David because he doesn’t like

jelly or marshmallow fluff. A sandwich with marshmallow fluff only was taken by Mariko, while

Kristen chose one with marshmallow fluff and peanut butter. Sam and Stephanie wanted a

sandwich with peanut butter and jelly as did Laura and Isabel and a jelly and fluff sandwich was chosen

by both Ty and Brandon.

Peanut

Butter

Peanut

Butter and

Jelly

Jelly Jelly and

Fluff

Fluff Peanut

Butter and

FluffDavid Laura Kenny Brandon Mariko Kristen

Kate Sam Oliver Ty

Stephanie

Isabel

The same information as the paragraph is shown in the table – which is easier to understand?

Frequency Distribution

A table that shows Classes/Intervals of data entries with a count of the number of entries in each class.

Frequency (f)

The number of data entries in a class

Class Frequency, f1 – 5 56 – 10 8

11 – 15 616 – 20 821 – 25 526 – 30 4

Example of a Frequency Distribution

Lower Class Limit

The smallest number that can belong to a class

Upper Class Limit

The largest number that can belong to a class

Class Width

The difference between consecutive Lower (or upper) limits in a class

Class Frequency, f1 – 5 56 – 10 8

11 – 15 616 – 20 821 – 25 526 – 30 4

Examples:1. What are the Lower Class Limits?

1, 6, 11, 16, 21, 26

Class Frequency, f1 – 5 56 – 10 8

11 – 15 616 – 20 821 – 25 526 – 30 4

Examples:2. What are the Upper Class Limits?

5, 10, 15, 20, 25, 30

Class Frequency, f1 – 5 56 – 10 8

11 – 15 616 – 20 821 – 25 526 – 30 4

Examples:3. What is the class width?

6 – 1 = 5

Range of the Data

The difference between the Highest number and the Lowest number in the Data set

Biggest # minus Smallest #

Construction a Frequency Distribution

1. Decide on the number of Classes to use Should be between 5 and 20

2. Find the class width

3. Find the Class Limits

4. Make a tally mark for each data entry in the row

5. Count the tally marks to find the total frequency, f, for each class

Finding the class width1. Determine the range of the data

2. Divide the range by the number of classes

3. Round up to the next convenient number

Finding the Class Limits

1. Use the smallest data entry as the Lower Limit of the 1st class.

2. To find the other Lower Limits, Add the class width to the previous lower limit. Continue doing this until you have all the lower limits.

3. Then find the Upper Limit of the first class, using the lower limits to guide you. Remember classes cannot overlap. Find the other upper limits in a similar manner.

1. The number of text messages received in one hour by 36 different students are listed below. Create a Frequency Table that has 5 classes.

2, 8, 10, 11, 16, 16, 25, 29, 1, 8, 12, 19, 20, 22, 29, 5, 7, 12, 17, 21, 26, 3, 9, 12, 17, 20, 22, 27,

23, 18, 13, 15, 6, 10, 5, 9

First: Find the Maximum and Minimum data entry 1 and 29

Second: Find the Range using these 2 entries 29 – 1 = 28

2, 8, 10, 11, 16, 16, 25, 29, 1, 8, 12, 19, 20, 22, 29, 5, 7, 12, 17, 21, 26, 3, 9, 12, 17, 20, 22, 27,

23, 18, 13, 15, 6, 10, 5, 9

Third: Find the class width (the problem asks for 5 classes)

28 5

= 5.6 Round to 6

The class width is 6

2, 8, 10, 11, 16, 16, 25, 29, 1, 8, 12, 19, 20, 22, 29, 5, 7, 12, 17, 21, 26, 3, 9, 12, 17, 20, 22, 27,

23, 18, 13, 15, 6, 10, 5, 9

4th: Find the Lower Limits (class width is 6)

The first lower limit is 1

(Now add 6 to this number to get the next one)

17131925

2, 8, 10, 11, 16, 16, 25, 29, 1, 8, 12, 19, 20, 22, 29, 5, 7, 12, 17, 21, 26, 3, 9, 12, 17, 20, 22, 27, 23, 18,

13, 15, 6, 10, 5, 9

Make table and put lower limits in it (keep in mind the problem asked for 5 classes – so you will need 5 rows.

Class Tally Frequency (f)

2, 8, 10, 11, 16, 16, 25, 29, 1, 8, 12, 19, 20, 22, 29, 5, 7, 12, 17, 21, 26, 3, 9, 12, 17, 20, 22, 27, 23, 18,

13, 15, 6, 10, 5, 9 Find the upper class limits by going 1 less than the next lower

limit

Class Tally Frequency (f)

1 – 6

7 – 12

13 – 18

19 – 24

25 – 30

2, 8, 10, 11, 16, 16, 25, 29, 1, 8, 12, 19, 20, 22, 29, 5, 7, 12, 17, 21, 26, 3, 9, 12, 17, 20, 22, 27, 23, 18,

13, 15, 6, 10, 5, 9

Using the numbers from the data set, put tallies in the appropriate row of the table and then add to get the Frequency

Class Tally Frequency (f)

1 – 6 llllll 6

7 – 12 lllllllllll 11

13 – 18 lllllll 7

19 – 24 lllllll 7

25 – 30 llll 5

2. The number of minutes 50 internet subscribers spent on the internet during their most recent session are listed below.

Create a Frequency Table that has 7 classes.

50, 40, 41, 17, 11, 7, 22, 44, 28, 21, 19, 23, 37, 51, 54, 42, 86, 41, 78, 56, 72, 56, 17, 7, 69, 30, 80, 56, 29, 33, 46, 31,

39, 20, 18, 29, 34, 59, 73, 77, 36, 39, 30, 62, 54, 67, 39, 31, 53, 44

First: Find the Maximum and Minimum data entry 7 and 86

Second: Find the Range using these 2 entries 86 – 7 = 79

Third: Find the class width

= 11.29 Round to 12

The class width is 12

50, 40, 41, 17, 11, 7, 22, 44, 28, 21, 19, 23, 37, 51, 54, 42, 86, 41, 78, 56, 72, 56, 17, 7, 69, 30, 80, 56, 29, 33, 46, 31, 39, 20,

18, 29, 34, 59, 73, 77, 36, 39, 30, 62, 54, 67, 39, 31, 53, 44

Fourth: Find all the lower limits – You need 7 classes

50, 40, 41, 17, 11, 7, 22, 44, 28, 21, 19, 23, 37, 51, 54, 42, 86, 41, 78, 56, 72, 56, 17, 7, 69, 30, 80, 56, 29, 33, 46, 31, 39, 20,

18, 29, 34, 59, 73, 77, 36, 39, 30, 62, 54, 67, 39, 31, 53, 44

Class Tally Frequency (f)

50, 40, 41, 17, 11, 7, 22, 44, 28, 21, 19, 23, 37, 51, 54, 42, 86, 41, 78, 56, 72, 56, 17, 7, 69, 30, 80, 56, 29, 33, 46, 31, 39, 20,

18, 29, 34, 59, 73, 77, 36, 39, 30, 62, 54, 67, 39, 31, 53, 44

Make table and put lower limits in it (keep in mind the problem asked for 7 classes – so you will need 7 rows.

Class Tally Frequency (f)

7 -19 - 31 - 43 – 55 -67 - 79 –

Find the upper class limits by going 1 less than the next lower limit

50, 40, 41, 17, 11, 7, 22, 44, 28, 21, 19, 23, 37, 51, 54, 42, 86, 41, 78, 56, 72, 56, 17, 7, 69, 30, 80, 56, 29, 33, 46, 31, 39, 20,

18, 29, 34, 59, 73, 77, 36, 39, 30, 62, 54, 67, 39, 31, 53, 44

Class Tally Frequency (f)

7 – 1819 – 3031 – 4243 – 5455 – 6667 – 78 79 – 90

50, 40, 41, 17, 11, 7, 22, 44, 28, 21, 19, 23, 37, 51, 54, 42, 86, 41, 78, 56, 72, 56, 17, 7, 69, 30, 80, 56, 29, 33, 46, 31, 39, 20,

18, 29, 34, 59, 73, 77, 36, 39, 30, 62, 54, 67, 39, 31, 53, 44

Class Tally Frequency (f)

7 – 18 XXXXXX 619 – 30 XXXXXXXXXX 1031 – 42 XXXXXXXXXXXXX 1343 – 54 XXXXXXXX 855 – 66 XXXXX 567 – 78 XXXXXX 679 – 90 XX 2

Using the numbers from the data set, put tallies in the appropriate row of the table and then add to get the Frequency

∑ f

Means the sum of all the Frequencies

To find this number, add all of the numbers in the frequency column together

∑ is Greek for “sum of”

The sum of the frequencies (∑ f) should Equal the number of data entries in the beginning problem

Class Tally Frequency (f)

7 – 18 XXXXXX 619 – 30 XXXXXXXXXX 1031 – 42 XXXXXXXXXXXXX 1343 – 54 XXXXXXXX 855 – 66 XXXXX 567 – 78 XXXXXX 679 – 90 XX 2

∑ f = 50

Homework

Worksheet 2.1 A