kk chap2 slides for bluman

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Frequency Distributions & Graphs ن ب ت ر و ر ك ت ز

Chapter # 2

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Objectives

1. Organize data using frequency distributions.

2. Represent data graphically using histograms,

frequency polygons and ogive.3. Represent data using bar chart, pareto chart

, pie graph and time series graph.

4. Draw and interpret a stem and leaf plot.

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Organizing data ت ن ب مظ

• Raw Data مخا تنا : When data are collected in

original form, they are called raw data

Marks of students:10,16, 20,25,28,30,35,45,52

Blood groups : A,B,AB+,A,A,B,B,O,B,O,AB+

• Frequency Distribution: is the organization of raw

data in a table form, using classes and frequencies

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10-20 2

20-30 12

30-40 30

40-50 10

50-60 3

اكرارة اوزت انت اخم نظم وهو جدول ف



Types of frequency distributions

VariablesQualitative Quantitative

nominal & ordinal discrete continuous

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اصنة اكرارة وزت

اكة انصة انت ف حة

اكة اصة انت ف حة

Categorical

frequency

distribution

Ungrouped freq

distribution

Grouped frequency

distribution



Types of frequency distributions1.Categorical

frequency distribution

2.Ungrouped 3.Grouped

frequency distribution frequency distribution

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5

Rating of a Hotel Number of Guests

Excellent 6

Very Good 19

Good 10

Poor 5

3 4

4 7

5 10

6 3

7 1

10-20 2

20-30 12

30-40 30

40-50 10

50-60 3

Types of frequency distributions



1.Categorical frequency distribution

Example 1: Blood groups of 30 students aregiven below construct the frequency

distribution and r

epresent it by a

.

BLOOD TYPE(Sample Size =30)

A , A ,B ,B ,AB+, A ,B ,AB+,O , A

B , A ,O , AB+,B ,AB+,B ,AB+,O ,B , A ,AB+,B ,B ,AB+,O ,B ,AB+,O ,AB+

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Raw data انت اخم



Pie Graph

Is a circle that is divided into sections

according to the percentage of

frequencies in each category of the

distribution

The purpose of the pie graph is toارضة

show ضو the relationshipةا of theparts ازجا to the wholeلكإ

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Relative frequency انس كرار سنا اكرار = كرار ائ ∕ جوع اكرار

Relative frequency = f/n

Sum of Relative Frequency = 1

اوي و حد س ب سن ل ت ر رك ل عوج

Degrees = f/n x 360º = زاوة اطع

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f/n x 100 = percentage

ائوة انسة

f/n x 360º = degreesعطا ةواز

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Categorical frequency distribution

Blood group frequency

Relative

frequency(f/n)

Percentage

f/n x 100= %

Angle of Circle

f/nx360º =degrees

A

BAB+

O

30 = n

6/30=0.20

1.00

0.2x100 = 20%

0.33x100 = 33%

0.3x100 = 30%

100%

0.2x360 = 72º

0.33x360 =11 9º

0.30x360 = 108º

360º

10/30=0.33

9/30=0.3

5/30=0.17 17.0% 0.167x360º=61º

6

10

9

5

Sample size [email protected] 10




Graphical presentation

A

6, 20%, 72º

B10, 33%, 119º

AB+ 9, 30%,

108º

O

5, -----%, -----º

Pie Chart

A

B

AB+

O

100%-83%=17% 360º-299º=61º

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Some questions on pie chart

• The missing percentage is

• The cumulative percentage for the third

part is

• The degree of the missing part is

• The sample size is

• The percentage of blood type AB+ is

100%-83%=17%

72º +119º+108º = 299º

360º-299º=61º

30

9/30x100=30%

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12



• If the frequency of AB+ is changed to 15 what willbe the percentage and degree of the angle

• The mode of the above data is

• The type of data in the above example is:a. continuous b. discrete c. ordinal d. nominal


Some questions on pie chart

f/n x100=15/30x100 = 50% f/nx360º=15/30x360º= 180º

Mode = 10



Categorical frequency distribution

Example 2: Guests staying at Holiday Inn were askedto rate the quality of their accommodations as beingexcellent, above average average, below average, or

poor . The ratings provided by a sample of 20 guests

are:( )

Below Average

Above Average

Above Average

Average

Above AverageAverage

Above Average

Average

Above Average

Below Average

Poor

Excellent

Above Average

Average

Above Average

Above Average

Below Average

Poor

Above AverageAverage

Average

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Poor

Below AverageAverage

Above Average

Excellent

2

35

9

1

Total 20

Rating FrequencyRelative freq

f/n

Percentage

f/nx100

2/20= 0.10

3/20 =0.15

5/20=0.25

9/20=0.45

1/20=0.05

1.00

0.10x100=10

0.15x100=150.25x100=25

0.45x100=45

0.05x100=05

100

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Poor BelowAverage

Average AboveAverage

Excellent

F r e q u e n c y

Rating

1

2

3

4

5

6

7

8

910

Holiday Inn Quality Ratings

2 3

5

9

1

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Questions on bar chart

1. What is the sample size?

2. What percentage of guests rated the

hotel average? 3. What is the cumulative percentage up

to average rating?


20

f/n=5/20x100=25%

10% +15%+25%=50%



Time Series Graphةبس ة لكش

Represents data that occur ثد ح over aspecified period of timeةد د ح ن ز فى فرة


Year Production

of cars

2006 12000

2007 12500

2008 13100

2009 13400

2010 12500

2011 13800Time on X-axis فا روحا

11000

11500

12000

12500

13000

13500

14000

2006 2007 2008 2009 2010 2011



Stem-and –Leaf Plot ةرل و ق سل طخمل


Retaining حظ the original valuesما خل تان ا ب ل whileshowing them in a graphic formتا وسر ةروص ى

The Stem and leaf plot is a method of organizing

data and is a combination of sorting and

graphing at the same time



1. Sort data in ascending order تنا رب

دص Marks obtained by 24 students in a statistics test:

19,22,25,26,27,28,29,30,34,36,37,42,43,44,46,48,

49,52,53,55,57,58,60

2. Separate the data according to the first digit.

19, 22,25,26,27,28,29, 30,34,36,37,

42,43,44,46,48,48,49 52,53,55,57,58, 60

19


Stem-and –Leaf Plot

Stem =1

رم اول اسق

Leaf =9

نثا رم اورة



2.Ungrouped frequency distributions

Example 1:Number of miles traveled by 16 teachers from

their houses to university.(data values are small)


10 , 4 ,4, 20, 20, 20, 10, 4, 4, 4, 20, 4, 10, 20, 4, 4

Class(X) Tallyتا Frequency(f) اكرار

Cumulativefrequency

Percentage(f/n)x100= %

4

10

20

Total n =

IIII III

IIIIIII

8

35

16 100%

8

8+3=1111+5=16

8/16X100=50%

3/16X100=19%5/16X100=31%



Example 2: The number of patients in the waiting

roomsرظناةفرغ within a hospital at a specific

time انة are given by the followingف وت

frequency distribution. ا وز اكراري ط

No of Room 1 2 3 4 5 Total

Frequency 3 5 11 ? 4 32

Answer the following questions:

1. The data can be represented graphically

by ……………………


2.Ungrouped frequency distributions

3 5

1

1 4



Class width/size ةئا لوط : Difference between

the two successive lower class limits or

the two successive upper class limits:

Class limits

5-910-14

15-19

20-24Class midpoint: Add the lower and upper limit and

divide by 2. midpoint =


Some basic terminology

19-14= 5

Class boundaries

4.5 – 9.5

9.5 – 14.5

14.5 – 19.5

19.5 – 24.5

=5+92

=7



Steps in the Construction of Grouped Freq

Distr

1. Find the highest(H) & lowest(L) value.

2. Find the rangeادى

. R = H – L

3. Select the number of classes دد ائت “K” Usually between 5 and 20 هم جد

4. Find the class width/sizeةئا لوط h = R/K(it is good to have “non-overlapping” classes)


ة اكر ة صر



Grouped Frequency DistributionMarks Freq(No of students) Class boundaries Mid pointsةئا زكر

10-14 1 9.5-14.5

15-19 2 14.5-19.5

20-24 5 19.5-24.5

25-29 10 24.5-29.5

30-34 7 29.5-34.5

35-39 4 34.5-39.5

40-44 1 39.5-44.5


(9.5+14.5)/2 = 24/2 = 12

34/2= 17

44/2= 22

54/2= 27

64/2= 32

74/2= 37

84/2= 42



Grouped frequency distribution

Classes(Grades) freq ClassBoundaries Mid points

10-14 1 9.5-14.5 12

15-19 2 14.5-19.5 17

20-24 5 19.5-24.5 22

25-29 10 24.5-29.5 27

30-34 7 29.5-34.5 32

35-39 4 34.5-39.5 37

40-44 1 39.5-44.5 42

30=

∑f

1

3+5=8

8+10=18

18+7=25

25+4=29

29+1=30

1+2=3

Cumulative frequency جا راركا




Histogram ير ك جرد

Frequency

اكرار

Class boundaries

اة حدود


X-axis

Y-axis



Frequency Polygon ضع ك ر

Frequency

اكرار

mid pointsةئا زكار


X-axis

Y-axis

Note: two additional points to be drawn with zero frequencies

one at the start & one at the end



Cumulative freq graph( ogive )

Cumulative Frequency

جا راركا

Class boundaries

اة حدود


X-axis

Y-axis



histogram


Y-axis

9.5 14.5 19.5 24.5 29.5 34.5 39.5 44.5

1

2

65

4

7

3

10

9

8

1 2

5

10

7

4

1

Class boundaries

f

r

e

q

u

e

n

c

y



Frequency polygon


Y-axis

9.5 14.5 19.5 24.5 29.5 34.5 39.5 44.5

1

2

65

4

7

3

10

9

8

1 2

5

10

7

4

1

Class boundaries

f

r

e

q

u

e

n

c

y



Grouped frequency distribution

Classes(Grades) freq ClassBoundaries Mid points

10-14 1 9.5-14.5 12

15-19 2 14.5-19.5 17

20-24 5 19.5-24.5 22

25-29 10 24.5-29.5 27

30-34 7 29.5-34.5 32

35-39 4 34.5-39.5 37

40-44 1 39.5-44.5 42

30=

∑f

1/30=0.033

5/30=0. 167

10/30=0.333

7/30=0.233

4/30=0.133

1/30=0.033

2/30=0.067

relative

frequency

f/∑f =f/n


1.000

Cumulative

relative freq

0.033

0.033+0.067=0.1

0.1+0.167=0.267

0.267+0.333=0.60

0.60+0.233=0.833

0.833+0.133=0.966

0.966+0.033=0.999



Histogram(relative freq )


Y-axis

9.5 14.5 19.5 24.5 29.5 34.5 39.5 44.5

0.05

0.10

0.30

0.25

0.20

0.35

0,15

0.033 0.067

0.167

0.333

0.233

0.133

0.033

Class boundaries

R

e

l

f

r

e

q



Frequency polygon(Relative Freq )


Y-axis

9.5 14.5 19.5 24.5 29.5 34.5 39.5 44.5

0.05

0.10

0.30

0.25

0.20

0.35

0.15

0.033 0.067

0.167

0.333

0.23

0.133

0.033

Class boundaries

R

e

l

a

t

i

v

e

f

r

e

q



Cumulative Relative freq graph(ogive)


Y-axis

9.5 14.5 19.5 24.5 29.5 34.5 39.5 44.5

0.20

0.40

1.00

0.80

0.60

0.033 0.100 0.267

0.60

0.833

0.966 0.999

Class boundaries

c

u

m

u

l

a

t

i

v

e

R

e

l

f

r

e

q



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Dept of Statistics KAU

khushnoorkhan64@yahoo com 36

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