The Frequency Table or Frequency Distribution Table What is it? Not a graph itself, but a prelude to an important statistical graph

The Frequency Tableor

Frequency Distribution Table

What is it? Not a graph itself, but a prelude

to an important statistical graph

2

What do Frequency Tables List?

A frequency distribution table for quantitative data lists, in table format, the following:

1. All classes of grouped data

2. Tallies of those classes

3. Frequencies of those classes

4. Relative frequencies of those classes

5. Grand total of # of classes, frequencies and relative frequencies

3

Frequency Table to Histogram

What do frequency tables enable statisticians to construct?

They enable construction of histograms

What do frequency tables enable statisticians to see?

They enable them to see how data naturally group into classes.

4

Discrete Frequency Table: ExampleSuppose there are 2000 families in a small town

and the distribution of children among them is as follows:

300 families have no children

400 families have 1 child

700 families have 2 children





Make a frequency table of the data

5

Discrete Frequency Table: ExampleFre- Relative

Class Tally quency Freq

A 0 Child

B 1 Children

C 2 Children

D 3 Children

E 4 Children

F 5 Children

G 6 Children

Totals 7 Classes

6

Discrete Frequency Table: ExampleFre- Relative


A 0 Child 300 0.15

B 1 Children 400 0.20

C 2 Children 700 0.35

D 3 Children 300 0.15

E 4 Children 100 0.05

F 5 Children 100 0.05

G 6 Children 100 0.05

Totals 7 Classes 2000 1.00

7

Making a Frequency Distribution Table

• I want to survey my classes on the subject of SIBLINGS. I want students to tell me the number of siblings that they have.

• The result will answer my question,

“What is the number of siblings for Intro Stats students in this period class?”

8

Discrete Frequency Tables

Each SIBLING represents a class of its own

SIBLING is a __________ _________ variable and so it is possible to make classes of only one value, which we will do in our survey. This will be one of the few examples of a single number class that we will explore.

9

Making a Frequency Distribution Table from a SurveyFre- Relative


A 0 siblings

B 1 siblings

C 2 siblings

D 3 siblings

E 4 siblings

F 5 siblings

G 6 siblings

H 7 siblings

I 8 siblings

J 9 siblings

K 10 siblings

Totals 11 Classes

10

Making a Frequency Distribution

Table from a Survey—Period 2

Intro Stats

Period 2

Sibling Survey Fre- Relative

Class quency Freq

A 0 siblings 5 14.7%

B 1 sibling 15 44.1%

C 2 siblings 10 29.4%

D 3 siblings 2 5.9%

E 4 siblings 2 5.9%

F 5 siblings

G 6 siblings

H 7 siblings

I 8 siblings

J 9 siblings

K 10 siblings

Totals 5 classes 34 100%

11



Intro Stats

Period 3


Class quency Freq

A 0 siblings 0 0.0%



D 3 siblings 5 17.2%

E 4 siblings 0 0.0%

F 5 siblings 1 3.4%

G 6 siblings

H 7 siblings

I 8 siblings

J 9 siblings

K 10 siblings


12



Intro Stats

Period 4


Class quency Freq

A 0 siblings 1 3.1%



D 3 siblings 5 15.6%

E 4 siblings 1 3.1%

F 5 siblings 1 3.1%

G 6 siblings 1 3.1%

H 7 siblings

I 8 siblings

J 9 siblings

K 10 siblings


13



Intro Stats

Period 5


Class quency Freq

A 0 siblings 4 11.8%



D 3 siblings 3 8.8%

E 4 siblings 4 11.8%

F 5 siblings 0 0.0%

G 6 siblings 1 2.9%

H 7 siblings 0 0.0%

I 8 siblings 1 2.9%

J 9 siblings

K 10 siblings


14


Table from a Survey—

4 Intro StatsClasses


Class quency Freq

A 0 siblings 10 7.8%B 1 sibling 56 43.4%C 2 siblings 36 27.9%D 3 siblings 15 11.6%E 4 siblings 7 5.4%F 5 siblings 2 1.6%G 6 siblings 2 1.6%H 7 siblings 0 0.0%I 8 siblings 1 0.8%J 9 siblingsK 10 siblings


15

Making a Dot Plot from a Survey—4

Intro Stats Classes

:

: Number of Siblings Per Student

: for Ms. H's Intro Stat Classes

: 21 Oct 2009

:

:

:

:

:

:

: :

: :

: :

: :

: :

: :

: :

: :

: :

: :

: : .

: : :

: : :

: : : :

: : : : .

: : : : :

: : : : :

: : : : : : : .

| | | | | | | | | | | | | |

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Source: In-Class Survey x-axis: # of Siblings

16

Discrete vs. Continuous Frequency TablesIn the sibling survey, each sibling represented a class

of its own

Sibling is a __________ ________ variable and so it is possible to make classes of only one value

However, most of the data we will be looking at will be of the continuous type

The next in-class survey will be “hair length” to the nearest inch—Hair Length is a _________ _________variable and so

Class widths will no longer be 1.

17

Frequency Distribution Table Definitions

What is a class on a frequency table?

One line on a frequency table

Determine these 2 things about Classes before constructing any Frequency Distribution Table:

1.Determine the starting point of the first class

2. Determine class widths before tallying begins

18

Making a Frequency Distribution Table

• I want to survey my classes on the subject of hair length. I want students to estimate the ‘average’ length of the hair on their heads. I want everyone to use the rulers available to measure their hair to the nearest 1”.

• This will help me answer the question, “How long is the average hair on an Intro Stats student in This Class?”

19

Making a Frequency TableFre- Relative

Class Tally quency Frequency

A 0"=x<3"

B 3"=x<6"

C 6"=x<9"

D 9"=x<12"

E 12"=x<15"

F 15"=x<18"

G 18"=x< 21"

H 21"=x<24"

I 24"=x<27"

J 27"=x<30"

K 30"=x<33"

Totals 11 Classes

20

Hair Length Survey (Oct 22, 2009) Results

Fre- Relative

Class quency Freq

A 0"=x< 3" 52 39.7%

B 3"=x< 6" 13 9.9%

C 6"=x< 9" 2 1.5%

D 9"=x< 12" 15 11.5%

E 12"=x<15" 24 18.3%

F 15"=x<18" 14 10.7%

G 18"=x< 21" 5 3.8%

H 21"=x<24" 2 1.5%

I 24"=x<27" 2 1.5%

J 27"=x<30" 0 0.0%

K 30"=x<33" 2 1.5%

Totals 11 Classes 131 100%

Results for 4 Intro Stat Classes

Dot Plot of Hair Length for 4 Classes

: Average Length of Hair per Student

: : for Ms. H's Intro Stat Classes

: : Oct 22, 2009

. : :

: : :

: : : .

: : : . : . : .

: : : : : : : : :

: : : : . : : : . : : : . :

: : : : : : . . : : : : : : : : : . : : : . . .

| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Source: In Class Survey x-axis: Length of Hair to the nearest inch

22

When?

When to use a frequency table?

When quantitative variables take on so many values (in so great a range or spread) that a graph of a distribution is clearer if nearby values are grouped together, or simply

when you want to draw a histogram.

23

Characteristics of the Classes in Frequency Table

1. Data is put in classes—A class could be 1 number or more than 1 number

2. Every class represents the same variable

3. Classes are not overlapping

4. Classes all have the same width

5. Classes vary from 4 to 10, depending on the spread of observations in the data set

24

Other Frequency Table DefinitionsClass Width

A class width is a distance: the first entry on the second line of a frequency table MINUS the first entry on the first line of a frequency table

Consistency in Class Widths

Class widths must ALWAYS be consistent for all classes in a frequency table

Number of Classes

The count of the # of lines that have been filled in on a frequency table, including zeroes if they are between filled-in lines.

25

% of Population over 65—DataAlabama 13 Louisiana 11 Ohio 13Alaska 5 Maine 14 Oklahoma 14Arizona 13 Maryland 11 Oregon 14Arkansas 15 Mass 14 Penn 16California 11 Michigan 12 R Island 16Colorado 10 Minnesota 12 S Carolina 12Connecticut 14 Mississippi 12 S Dakota 14Delaware 13 Missouri 14 Tennessee 13Florida 19 Montana 13 Texas 10Georgia 10 Nebraska 14 Utah 9Hawaii 13 Mevada 11 Vermont 12Idaho 11 N Hampshire 12 Virginia 11Illinois 13 N Jersey 14 Washington 12Indiana 13 N Mexico 11 W Virginia 15Iowa 15 N York 13 Wisconsin 13Kansas 14 N Carolina 13 Wyoming 11Kentucky 13 N Dakota 15

26

% of Population over 65—Dot Plot

Percent of Population over 65 years of Agein the 50 States

.: : :

: . : :: : : :

. : : : : :. . : : : : : : : .

| | | | | | | | |4 6 8 10 12 14 16 18 20

Source: Statistical Abstract of the USx-axis: Number in % to nearest integer

27

% of Population over 65—DataFre- Rel


A 4 x < 6 %

B 6 x < 8 %

C 8 x < 10 %

D 10 x < 12 %

E 12 x < 14 %

F 14 x < 16 %

G 16 x < 18 %

H 18 x < 20 %

Totals

28

% of Population over 65—DataFre- Rel


A 4 x < 6 % I 1 0.02

B 6 x < 8 % 0 0 0.00

C 8 x < 10 % I 1 0.02

D 10 x < 12 % IIIII IIIII I 11 0.22

E 12 x < 14 % IIIII IIIII IIIII IIII 20 0.40

F 14 x < 16 % IIIII IIIII IIIII 14 0.28

G 16 x < 18 % II 2 0.04

H 18 x < 20 % I 1 0.02

Totals 50 50 1.00

29

Student Scores Basic Algebra—DataHere is a set of final grades in Basic Algebra class by percentage for 43 studentsMina 73 Jordan 80 David 83Travis 81 Lauren 73 Audrey 72Jenny 70 Max 58 Jessie 90Lisa 71 Shelby 89 Eric 83Jordan 74 Megan 71 Gurveer 72Joanne 74 Joel 79 Tyler 91Michelle 72 Kyle 67 Zaid 82Aaron 72 Michael 81 Sean 53Brett 87 Owen 78 Carolyn 84Yingmin 90 Cameron 82 Niki 72Stephie 87 Jeremy 78 Joshua 84Andrew 84 Ken 88 John 74Sabreen 70 Jeff 80 Chris 85Stacey 73 Anna 75 Source: Smith, Barbara.Tong 68 Diana 66 Algebra 2008

30

Student Scores in Basic Algebra—Freq Table

Complete the Frequency Table: Fre- Rel


A 52 x% < 57

B 57 x% < 62

C 62 x% < 67

D 67 x% < 72

E 72 x% < 77

F 77 x% < 82

G 82 x% < 87H 87 x% < 92

Totals

31

Student Scores in Basic Algebra—Freq Table

Fre- Rel

Class Tally quency Freq (% nrst 0.1)

A 52 x% < 57 I 1 2.3%

B 57 x% < 62 I 1 2.3%

C 62 x% < 67 I 1 2.3%

D 67 x% < 72 IIII I 6 14.0%

E 72 x% < 77 IIII IIII II 12 27.9%

F 77 x% < 82 IIII II 7 16.3%

G 82 x% < 87 IIII III 8 18.6%

H 87 x% < 92 IIII II 7 16.3%

# of classes 8 Totals 43 100%

32

Student Scores Basic Algebra—Dot Plot

Final Grades in Basic Algebra Class for Ms. Barbara Smith, 2008

. : . . .

. . . . : : : : : . : . : : : : : . : . : .| | | | | | | | | | | | | | | | | | | | |

52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92Source: Ms. Barbara Smith x-axis: Score in percent

33

The Number of Cell Phones in your Household

I want to survey my classes on the subject of CELL PHONES. I want students to tell me the number of operating cell phone that are located in their household, including cell phones for parents (both personal and work cell phones), siblings, etc.

The result will answer my question, “What is the number of CELL PHONES for

the household of Intro Stats students in this period class?”

34

Discrete vs. Continuous Frequency Tables

Today, we will conduct a survey in class, counting the number of cell phones per household.

As you take notes, please think about how many cell phones are used in your household.

Cell Phone is a ________ ________ variable, so it is possible to make classes of only one value.

35

The Conventions of Writing Classes for Frequency Tables with Discrete Quantitative Variables

Rules or Conventions for Discrete Classes (such as cell phones & siblings):

1. Inequalities are not required when class width is 1

2. If class width is > 1, use the rules for continuous classes

3. Data may never fall into more than 1 class

36

How to Write Classes for Discrete Quantitative Variables

ExampleIn a survey of cell phones in a family, each quantity

could become its own classClass A 0 cell phones Class B 1 cell phone Class C 2 cell phones

Or we could group this data into wider classes Class A 0 ≤ x < 2 cell phonesClass B 2 ≤ x < 4 cell phonesClass C 4 ≤ x < 6 cell phones

37

Data: Number of

Cell Phones in

Your Household

First Name Number of First Name Number ofCell Phones Cell Phones

1 19

2 20

3 21

4 22

5 23

6 24

7 25

8 26

9 27

10 28

11 29

12 30

13 31

14 32

15 33

16 34

17 35

18 36

38

Frequency Table:

Number of Cell

Phones in Your

Household

Fill in the frequency table for your class: (Class width is 1 and starting pt is 0)

Cell Phone Survey Tally Frequency Relative Frequency

cell phones

cell phones

cell phones

cell phones

cell phones

cell phones

cell phones

cell phones

cell phones

cell phones

cell phones

# of classes Totals

Spread for Cell Phones Range for Cell Phones

Mean for Cell Phones Median for Cell Phones

n = Mode for Cell Phones(& # of times it appears)

Class width

39

Discrete vs. Continuous Frequency Tables

What class width did you use?

How many classes did you have?

Did you need to use inequalities to describe the class?

40

Dot Plot:Number of Cell

Phones in Your

Household

# of 'Working' Cell Phones in the Households

of Ms. H's Intro Stat Classes

| | | | | | | | | | | | | | | | | | |

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Source: In Class Survey x-axis: # of Cell Phones

41

Frequency Table:

Number of Cell

Phones in Your

Household

Period 1

Cell Phone Survey Fre- Relative

Class quency Freq

A 0 cell phones 0 0.0%

B 1 cell phones 0 0.0%

C 2 cell phones 1 3.0%

D 3 cell phones 8 24.2%

E 4 cell phones 11 33.3%

F 5 cell phones 7 21.2%

G 6 cell phones 4 12.1%

H 7 cell phones 2 6.1%

I 8 cell phones 0 0.0%

J 9 cell phones 0 0.0%

K 10 cell phones 0 0.0%


42

Frequency Table:

Number of Cell

Phones in Your

Household

Period 2


Class quency Freq













43

Frequency Table:

Number of Cell

Phones in Your

Household

Period 4


Class quency Freq













44

Frequency Table:

Number of Cell

Phones in Your

Household

Period 6


Class quency Freq













45

Frequency Table:

Number of Cell Phones

in 4 Classes’

Households

Cell Phone Survey In ClassResults for 4 Classes


Class quency Freq













46

Dot Plot:Number of Cell

Phones in Your

Household

.

:

:

:

: Number of Cell Phones Per

: Student Household

: for Ms. H's 4 Intro Stat Classes

:

:

:

: :

: :

: :

: : :

: : :

: : :

: : :

: : : :

: : : :

: : : :

: : : :

. : : : : .

: : : : : :

. : : : : : : :

| | | | | | | | | | | | | |

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Source: In-Class Survey x-axis: # of Cell Phones

47

The Conventions of Writing Classes for Frequency Tables with Continuous Quantitative Variables

Rules or Conventions for Continuous Classes:

1. The first inequality ALWAYS is a less than or equal (≤) sign

2. The second inequality is always a less than sign (<)

3. An x is written in between the two signs

4. ‘x’ should be defined

5. Data may NEVER fall into more than one class

Example

In a hair length survey, our first class might be 0”≤x<3”

Next class might be 3”≤x<6”, etc.

48

Spending by Shoppers at Safeway—Data

Shopper $ Shopper $ Shopper $

spent spent spent

1 18 11 20 21 212 24 12 26 22 283 36 13 13 23 444 18 14 19 24 165 25 15 28 25 226 38 16 43 26 287 19 17 13 27 178 26 18 20 28 239 39 19 28 29 32

10 11 20 15 30 1731 24

49

Spending by Shoppers at Safeway—Frequency Table

RelativeClass Tally Frequency Frequency

A

B

C

D

E

F

G

H

Total

50

Spending by Shoppers at Safeway—Frequency Table

RelativeClass Tally Frequency Freq (% nrst 0.1)

A $10=x<$15 III 3 9.7%

B $15=x<$20 IIII III 8 25.8%

C $20=x<$25 IIII II 7 22.6%

D $25=x<$30 IIII II 7 22.6%

E $30=x<$35 I 1 3.2%

F $35=x<$40 III 3 9.7%

G $40=x<$45 II 2 6.5%

H

# of Classes 7 Total 31 100.0%

51

Spending by Shoppers at Safeway—Data

Amount Spent at Safeway by 31 Consecutive Shoppers June 5, 2009

:

. : . . : : : : . . . : . : : . . . . . .| | | | | | | | | | | | | | | | | |

10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44Source: A researcher x-axis: $

52

Loss of Wetlands—Data

State % State % State % State %

# Lost # Lost # Lost # Lost

1 46 13 46 25 87 37 742 87 14 90 26 20 38 333 27 15 60 27 56 39 504 35 16 42 28 52 40 495 48 17 27 29 42 41 356 37 18 9 30 50 42 567 52 19 72 31 73 43 288 91 20 46 32 39 44 499 23 21 81 33 30 45 67

10 38 22 38 34 59 46 5011 36 23 54 35 89 47 3112 24 24 85 36 59 48 35

53

Loss of Wetlands—Data Class Tally Frequency Rel Frequ

A

B

C

D

E

F

G

H

# of Classes Total

54


Class Tally Frequency Rel Frequ

A 0%=x<12% I 1 2.1%

B 12%=x<24% II 2 4.2%

C 24%=x<36% IIII IIII 10 20.8%

D 36%=x<48% IIII IIII 10 20.8%

E 48%=x<60%IIII IIII III 13 27.1%

F 60%=x<72% II 2 4.2%

G 72%=x<84% IIII 4 8.3%

H 84%=x<96% IIII I 6 12.5%

# of Classes 8 Total 48 100%

55


% of Wetlands lost in last 200 years

. . .

. . . . : . . . . : . . : . : : . : :| | | | | | | | | | | | | | | | | | | | | |8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Source: Environmental Almanac x-axis: % of wetlandslost to the nrst %

: . : : . . . . . . . : . . .

| | | | | | | | | | | | | | | | | | | | |

52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92

56

Tree Circumference—Data

Tree Circum Tree Circum Tree Circum Tree Circum

# in mm # in mm # in mm # in mm

1 108 13 106 25 115 37 120

2 106 14 119 26 125 38 116

3 103 15 101 27 112 39 108

4 114 16 99 28 106 40 114

5 91 17 108 29 83 41 117

6 122 18 105 30 117 42 105

7 99 19 102 31 120 43 91

8 111 20 109 32 108 44 117

9 114 21 99 33 120 45 10010 105 22 122 34 113 46 122

11 102 23 110 35 90 47 117

12 113 24 112 36 122 48 115

57

Tree Circumference—Blank Rel Frequency Table Class Tally Frequency Rel Freq

A

B

C

D

E

F

G

H

# of Classes Total

58

Tree Circumference—Frequency Dist Table Class Tally Frequency Rel Freq

A 80=x<88mm I 1 2.1%

B 88=x<96mm III 3 6.3%

C 96=x<104mm IIII III 8 16.7%

D 104=x<112mm IIII IIII III 13 27.1%

E 112=x<120mm IIII IIII IIII 15 31.3%

F 120=x<128mm IIII III 8 16.7%

G

H

# of Classes 6 Total 48 100%

59

Temperatures in Alaska—Data

Date Temp. Date Temper Date Temper

in F° in F° in F°

1 Jan 41 11 37 21 372 Jan 35 12 39 22 37

3 30 13 34 23 394 40 14 43 24 465 33 15 50 25 456 34 16 42 26 397 33 17 43 27 398 40 18 38 28 429 40 19 42 29 35

10 40 20 45 30 3831 42

60

Temperatures in Alaska—Frequency Table

RelativeClass Tally Frequency Frequency

A

B

C

D

E

F

G

H

Total

61

Temperatures in Alaska—Frequency TableRelative

Class Tally Frequency Frequency

A 30=x<33° I 1 0.032

B 33=x<36° IIII I 6 0.194

C 36=x<39° IIII 5 0.161

D 39=x<42 IIII IIIII 9 0.290

E 42=x<45° IIII I 6 0.194

F 45=x<48° II 3 0.097

G 48=x<51° I 1 0.032

H

Total 31 1.000

62

Temperatures in Alaska—Dot Plot

Daily Maxiumum Termperaturesin January in Fairbanks, Alaska

. :. : : : : : :

28 29 30 31 32 33 34 35 36 37 38 39

: :: . : : : . .

40 41 42 43 44 45 46 47 48 49 50 51Source: Alaskan Weather Bureaux-axis: temperature in degrees F

63

Super Bowl Attendance—Data

SuperAttendance Super Attendance Super Atten

Bowl in (,000) Bowl in (,000) Bowlin(,000)

I 62 XI 103 XXI 101II 76 XII 76 XXII 73III 75 XIII 79 XXIII 75IV 81 XIV 104 XXIV 73V 79 XV 76 XXV 74VI 81 XVI 81 XXVI 63VII 90 XVII 104 XXVII 98VIII 72 XVIII 73 XXVIII 73IX 81 XIX 84 XXIX 74X 80 XX 74 XXX 76

XXXI 72

64

Super Bowl Attendance—Frequency Table

Class Tally FrequencyRel Freq

A

B

C

D

E

F

Totals

65

Super Bowl Attendance—Frequency Table

Class Tally Frequency Rel Freq

A 60 = x < 70 II 2 0.065

B 70 = x < 80 IIII IIII IIII II 17 0.548

C 80 = x < 90 IIII I 6 0.194

D 90 = x < 100 II 2 0.065

E 100 = x < 110 IIII 4 0.129

F

Total 31 1.000

66

Super Bowl Attendance—Dot Plot

Attendance at Super Bowl Games I - XXXI

: : :. . : : : : : . : . : .

| | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89

. . . . : .| | | | | | | | | | | | | | | | | | | | |

90 91 92 93 94 95 96 97 98 99100101102103104105106107108109110

x-axis: attendance in ,000Source: National Football League

Documents

The Frequency Table or Frequency Distribution Table What is it? Not a graph itself, but a prelude to an important statistical graph