chapter 2 data collection and presentation business statistics

UNIT TWO
DATA COLLECTION
&
PRESENTATION

Types of Data
Data sets can consist of two types of data:
Qualitative data and Quantitative data.
DATA
Qualitative Data
Consists of
attributes, labels, or
nonnumeric entries.
Quantitative Data
Consists of numerical
measurements or
counts.

Qualitative and Quantitative Data
Example: The grade point averages of five
students are listed in the table. Which data are
qualitative data and which are quantitative data?
Student GPA
Sara 3.22
Berhan 3.98
Mahlet 2.75
Tsehay 2.24
Hana 3.84
Quantitative data
Qualitative data

Levels of Measurement
•The level of measurement determines which
statistical calculations are meaningful.
•Measurement is the assignment of values to
objects or events in a systematic fashion. The
four levels of measurement are: nominal, ordinal,
interval, and ratio.
Lowest
to
highest
Levels of
Measurement
Nominal
Ordinal
Interval
Ratio

Nominal Scale
• The values of a nominal attribute are just different
names, i.e., nominal attributes provide only enough
information to distinguish one object from another.
• Qualities with no ranking or ordering; no numerical or
quantitative value. These types of data consists of
names, labels and categories.
• It is a scale for grouping individuals into different
categories.
Example : Eye color: brown, black, etc,
Sex: Male, Female.
• In this scale, one is different from the other.
• Arithmetic operations (+, -, *, ÷) are not applicable,
comparison (<, >, ≠, etc) is impossible.

Ordinal Scale
• Defined as nominal data that can be ordered or ranked.
• Can be arranged in some order, but the differences
between the data values are meaningless.
• Data consisting of an ordering of ranking of measurements
are said to be on an ordinal scale of measurements.
• It provides enough information to order objects.
• One is different from and greater /better/ less than the
other.
• Arithmetic operations (+, -, *, ÷) are impossible,
comparison (<, >, ≠, etc) is possible.
Example: Letter grading (A, B, C, D, F),
 Rating scales (excellent, very good, good, fair, poor),
 Military status (general, colonel, lieutenant, etc).

Interval Level
• Data are defined as ordinal data and the differences
between data values are meaningful. However, there is no
true zero, or starting point, and the ratio of data values are
meaningless.
• Note: Celsius & Fahrenheit temperature readings have no
meaningful zero and ratios are meaningless. For example, a
temperature of zero degrees (on Celsius and Fahrenheit
scales) does not mean a complete absence of heat.
• One is different, better/greater and by a certain amount of
difference than another.
• Possible to add and subtract. For example; 800c – 500c =
300c, 700c – 400c = 300c.
• Multiplication and division are not possible. For example;
600
c = 3(200
c). But this does not imply that an object which
is 600
c is three times as hot as an object which is 200
c.
• Most common examples are: IQ, temperature.

Ratio Scale
• Similar to interval, except there is a true zero
(absolute absence), or starting point, and the
ratios of data values have meaning.
• Arithmetic operations (+, -, *, ÷) are applicable.
For ratio variables, both differences and ratios
are meaningful.
• One is different/larger /taller/ better/ less by
a certain amount of difference and so much
times than the other.
• This measurement scale provides better
information than interval scale of measurement.
• Example : weight, age, number of students.

Summary of Levels of Measurement
Levels of measurement
Nominal Ordinal Interval Ratio
Put data in categories Yes Yes Yes Yes
Arrange data in order No Yes Yes Yes
Subtract data values No No Yes Yes
Determine if one data
value is a multiple of
another
No No No Yes

Data Collection
 Is a systematic and meaningful assembly of
information for the accomplishment of
the objective of a statistical
investigation.
 It refers to the methods used in
gathering the required information from
the units under investigation.

Terminologies
• A simulation is the use of a
mathematical or physical model to
reproduce the conditions of a situation
or process.
•A survey is an investigation of one or
more characteristics of a population.
A census is a measurement of an
entire population.
A sampling is a measurement of part
of a population.

Methods of Data Collection
Stratified Samples
 A stratified sample has members from
each segment of a population.
 This ensures that each segment from the
population is represented.
Freshme
n
Sophomor
es
Juniors Seniors

Cluster Samples
 A cluster sample has all members from
randomly selected segments of a
population.
Freshme
n
Sophomor
es
Juniors Seniors

Systematic Samples
A systematic sample is a sample in which each
member of the population is assigned a number. A
starting number is randomly selected and sample
members are selected at regular intervals.
Every fourth member is chosen.

Convenience Samples
• A convenience sample consists only of
available members of the population.
•Convenience sampling is sometimes referred to
as haphazard or accidental sampling.
•Sample units are only selected if they can be
accessed easily and conveniently.
•Although useful applications of the technique
are limited, it can deliver accurate results when
the population is homogeneous.
•May not be representative of the target
population result in the presence of bias.

Quota sampling
• Quota sampling
• Snowball Sampling

PRIMARY AND SECONDARY DATA
PRIMARY DATA/ SOURCES
 A primary source is a source from where first-hand
information is gathered.
 Are original sources of data.
SECONDARY DATA
 Is the one that makes data available, which were
collected by some other agency.
 A source, which is not primary, is necessarily a
secondary source.
 Obtained from such sources as census and survey
reports, books, official records, reported experimental
results, previous research papers, bulletins, magazines,
newspapers, web sites, and other publications.

EXAMPLE
 A study conducted to see the age
distribution of HIV/AIDS victim
citizens.
 Information obtained from the victim
citizens are primary sources.
 Use of records of hospitals and other
related agencies to obtain the age of
the victim citizens without the need of
tracing the victims personally is a
secondary source.

Advantages and Disadvantages of Primary &
Secondary data
Advantages of primary data over that
of secondary data.
 Gives more reliable, accurate and
adequate information, which is
suitable to the objective and purpose
of an investigation.
 Shows data in greater detail.
 Free from errors that may arise from
copying of figures from publications,
which is the case in secondary data.

DISADVANTAGES OF PRIMARY DATA
 It is time consuming and costly.
 Gives misleading information due to lack of
integrity of investigators and non-
cooperation of respondents.
ADVANTAGE OF SECONDARY DATA:
• It is readily available and hence convenient
and much quicker
• It reduces time, cost and effort as
compared to primary data.
• May be available in subjects (cases) where it
is impossible to collect primary data. Such a
case can be regions where there is war.

The disadvantages of Secondary data :
 Data obtained may not be sufficiently
accurate.
 Data that exactly suit our purpose may not
be found.
 Error may be made while copying figures.

The choice between primary data and
secondary data is determined by factors
 Nature and scope of the enquiry,
 Availability of financial resources,
 Availability of time,
 Degree of accuracy desired
 Primary data are used in situations where
secondary data do not provide adequate basis
of analysis. i.e. when the secondary data do
not suit a specific investigation.
 Unless for such cases, most statistical
investigations rest up on secondary data since
it minimizes cost and saves time.

Methods of collecting primary data
1. Personal Enquiry Method (Interview
method)
A. Direct Personal Interview: There is a face-
to-face contact with the persons from
whom the information is to be obtained.
B. Indirect Personal Enquiry (Interview): The
investigator contacts third parties called
witnessed who are capable of supplying the
necessary information.
2. Direct Observation
3. Questionnaire method

METHODS /TYPES OF CLASSIFICATION
Region Dominant Language Spoken
East Africa Amharic
West Africa French
North Africa Arabic
South Africa English
Geographical Classification: - Data are
arranged according to places like continents,
regions, and countries.

Chronological Classification:- Data are
arranged according to time like year, month.
Year (in EC) Population (in million)
1974 30
1986 52
1991 60

•Qualitative Classification: - Data are
arranged according to attributes like color,
religion, marital-status, sex, educational
background, etc.
Employees in Factory X
Educated
Male Female
Uneducated
Male Female

•Quantitative Classification:- The
statistical data is classified according to
some quantitative variables. The variable
may be either discrete or continuous.
Mr. x Height (X) in cm
A 160
B 182
C 175
D 178

Discrete Variables – are variables that
are associated with enumeration or
counting.
Example
Number of students in a class
Number of children in a family, etc
•Continuous Variables – are variables
associated with measurement.
Example
 Weights of 10 students.
 The heights of 12 persons.
 Distance covered by a car between
two stations etc.

FREQUENCY DISTRIBUTION
Frequency refers to the number of
observations a certain value occurred
in a data.
A frequency distribution is the
organization of raw data in table
form, using classes and frequencies.
The tabular representation of values
of a variable together with the
corresponding frequency is called a
Frequency Distribution (FD).

A.Ungrouped Frequency Distribution (UFD)
Shows a distribution where the values of a variable are
linked with the respective frequencies.
Example: Consider the number of children in 15
families
No. of Children
(Values)
No. of Family
(Tallies)
Frequency
0 / / 2
1 //// 4
2 //// 4
3 / / / 3
4 / / 2
Total 15

A.Grouped Frequency Distribution (GFD)
If the mass of the data is very large, it is
necessary to condense the data in to an
appropriate number of classes or groups of
values of a variable and indicate the number of
observed values that fall in to each class.
A GFD is a frequency distribution where
values of a variable are linked in to groups &
corresponded with the number of observations
in each group.
Values (xi)
1 - 25 26 - 50 51 - 75 76 - 100
Frequency (fi)
3 10 18 6

COMMON TERMINOLOGIES IN A GFD
i. Class:- group of values of a variable between
two specified numbers called lower class limit
(LCL) & upper class limit (UCL)
Class limits (CL): It separates one class from
another. The limits could actually appear in the
data and have gaps between the upper limits of
one class and the lower limit of the next class.
In Example*, the GFD contains four classes:
1 – 25, 26 – 50, 51 – 75, and 76 – 100

Class boundaries: Separate one class in a
grouped frequency distribution from the other.
The boundary has one more decimal place than
the raw data.
•There is no gap between the upper boundaries
of one class and the lower boundaries of the
succeeding class.
•Obtained by subtracting half of the unit of
measurement (u) from the lower limits and by
adding ½ (u) on the upper limits of a class. U can
assume values 1, 0.1, 0.01, 0.001……
i.e UCBi = UCLi + ½ (u)
LCBi = LCLi - ½ (u)
Where UCBi = Upper Class Boundaries and

ii. Class Frequency (or Simply
Frequency): refers to the number of
observations corresponding to a class.
In Example * The class frequency of the
1st
, 2nd
, 3rd
, & 4th
classes are respectively
3, 10, 18 and 6.

Note: The unit of measurement (u) is the gap
between any two successive classes. i.e
u = lower limit of a class – upper limit of the
preceding class.
In Example *, consider the 2nd
class, 26 – 50, since u =
26 – 25 = 1,
LCL2
= 26 UCL2
= 50
LCB2
= 26 - ½(1) = 25.5 UCB2
= 50 + ½(1) =50.5
iv. Class Width (size of a class or class
interval): it is the difference between the upper
and lower class limits or the difference between
the upper and lower class boundaries of any
class.

Remarks:
1. If both the LCL & UCL are included
in a class, it is called an inclusive
class. For inclusive classes,
Class width (cw) = UCBi
- LCBi
2. If LCL is included and the UCL is
not included in a class, it is called an
exclusive class. For exclusive
classes;
Class width (cw) = UCLi
– LCLi
To be consistent, we use inclusive
classes.

v. Class Mark (cm): it is the mid point
(center) of a class
Note:- the difference between any two
successive class marks is equal to the
width of a class
Range (R) : is the difference between the
largest (L) and the smallest (S) values in a
data
R = L – S

RULES FOR FORMING A GROUPED FREQUENCY DISTRIBUTION
To construct a GFD the following points should be
considered
1. The classes should be clearly defined. That is
each observation should fall in to one & only
one class.
2.The number of classes neither should be too
large nor too small. Normally, 5 to 20 classes
are recommended.
3.All the classes should be of the same width.
An approximate suitable class width can be
obtained as:

Note that a suitable number of classes can be
obtained by using the formula
n  1 + 3.322 logN.
up/down to the nearest whole number, where
N is the total number of observations.
 Alternatively n can also be determined by
formula
Where
n=Number of Classes
N=Total number of observations

4.Determine the class limits
 Determine the lower class limit of the first
class (LCL1), then
• LCL2 = LCL1 + cw, LCL3 = LCL2 + cw,… LCLi+1 = LCLi + cw
 Determine the upper class limit of the first
class (UCL1) i.e.
UCL1 = LCL1 + cw – u,
 where u = the unit of measurement, then
UCL2 = UCL1 + cw , UCL3 UCL2, … , UCLi+1 = UCLi + cw
 Complete the GFD with the respective class
frequencies.

• Example. The number of customers
for consecutive 30 days in a
supermarket was listed as follows:
20 48 65 25 48 49
35 25 72 42 22 58
53 42 23 57 65 37
18 65 37 16 39 42
49 68 69 63 29 67
A.Construct a GFD with a suitable number of
classes
B.Complete the distribution obtained in (A)
with class boundaries & class marks

Solution: i. Range = Largest value –
smallest value
= 72 – 16 = 56
N = 30 (total number of observations)
 number of classes, n = 1 + 3.322 log30
 n = 1 + 3.322 log30
= 1 + 3.322 (1.4771)
= 5.9
• Hence a suitable number of class n
is chosen to be 6

 Class width = 9.33 = cw
 For the sake of convenience, take
cw to be 10 (note that it is also
possible to choose the cw to be 9).
• Take lower limit of the 1st
class (LCL1)
to be 16 & u = 1
• i.e. LCL1 = 16 and UCL1 = LCL1 + cw – u =16+10-1 = 25
LCL2 = LCL1 + cw = 16 + 10 = 26 UCL2 = UCL1 + cw = 25 + 10 = 35
LCL3 = LCL2 + cw = 26 + 10 = 36 UCL3 = UCL2 + cw = 35 + 10 = 45
• Therefore, the GFD would be

Class (xi) Frequency (fi)
16 – 25 7
26 – 35 2
36 – 45 6
46 – 55 5
56 – 65 6
66 – 75 4
A)
B)
Class (xi) Frequency (fi) CBi cmi
16 – 25 7 15.5 – 25.5 20.5
26 – 35 2 25.5 – 35.5 30.5
36 – 45 6 35.5 – 45.5 40.5
46 – 55 5 45.5 – 55.5 50.5
56 – 65 6 55.5 – 65.5 60.5
66 – 75 4 65.5 – 75.5 70.5

CUMULATIVE FREQUENCY DISTRIBUTION (CFD)
 Cumulative frequency (CF): It is the
number of observation less than the
upper class boundary or greater than
the lower class boundary of class.
 ‘Less Than’ Cumulative Frequency
Distribution (<CFD): it is the number of
values less than the upper class
boundary of a given class.
 ‘More Than’ Cumulative Frequency
Distribution (>CFD): it is the number
of values greater than the lower class
boundary of a given class.

Example : Consider the frequency distribution
given below
Class (xi) Frequency (fi) Less than
Cumulative
Frequency (<cfi)
More than
Cumulative
Frequency (>cfi)
3 – 6 4 4 30
7 – 10 7 11 26
11 – 14 10 21 19
15 – 18 6 27 9
19 – 22 3 30 3
This means that from ‘less than’ cumulative
frequency distribution there are 4 observations
less than 6.5, 11 observations below 10.5, etc and
from ‘more than’ cumulative frequency
distribution 30 observations are above 2.5, 26
above 6.5 etc.

RELATIVE FREQUENCY DISTRIBUTION (RFD)
• It enables the researcher to know the proportion or
percentage of cases in each class.
• Obtained by dividing the frequency of each class by
the total frequency. It can be converted in to a
percentage frequency by multiplying each relative
frequency by 100%. i.e.
• Where Rfi – is the relative frequency of the ith class
fi – is the frequency of the ith
class
n – is the total number of observations
Note: Pfi = Rfi  100%
• Where Pfi is percentage frequency of each class.

Example : The relative and percentage frequency
distribution of is :
xi fi Rfi %freq. (Pfi)
3 – 6 4 4/30 0.13 4/30  100
7 – 10 7 7/30 0.23 7/30  100
11 – 14 10 10/30 0.33 10/30  100
15 – 18 6 6/30 0.20 6/30  100
19 – 22 3 3/30 0.10 3/30  100
Total 30 1 100% 100%
Relative cumulative frequency (RCf): The running total
of the relative frequencies or the cumulative frequency
divided by the total frequency gives the percent of the
values which are less than the upper class boundary or
the reverse.
CRfi = Cfi/n= Cfi/∑fi

PRESENTATION OF DATA
• Presentation is a statistical procedure of arranging
and putting data in a form of tables, graphs, charts
and/or diagrams.
HISTOGRAM
• Consisting of a series of adjacent rectangles whose
bases are equal to the class width of the
corresponding classes and whose heights are
proportional to the corresponding class frequencies.
• The class boundaries are marked along the x – axis
and the class frequencies along the y – axis.
• It describes the shape (symmetry) of the data and
where do most of the data values lie?

• Example : A histogram to representing
the following data.
Class limits 15-24 25-34 35-44 45-54 55-64 65-74 75-84
Frequency 3 4 10 15 12 4 2
Histogram
3
4
10
15
12
4
2
0
5
10
15
20
Class width
Frequency

FREQUENCY POLYGON
• It is a line graph of frequency
distribution.
• Clearly illustrates shape of the data
than a histogram does.
• Connects the centers (class marks)
of the tops of the histogram bars
with a series of straight lines.

9.5 19.5 29.5 39.5 49.5 59.5 69.5 79.5 89.5
0
2
4
6
8
10
12
14
16
Frequency Polygon
Class mark
F
r
e
q
u
e
n
c
y

CUMULATIVE FREQUENCY CURVE, (OGIVE)
• It is useful for determining the number
of values below or above some particular
value.
• Uses class boundaries along the
horizontal axis and frequencies along the
vertical axis.
• There are two type of O-give namely less
than Ogive and more than Ogive.

CUMULATIVE FREQUENCY CURVE, (OGIVE)
The Less thanOgive
0
10
20
30
40
50
60
14.5 24.5 34.5 44.5 54.5 64.5 74.5 84.5
Class Boundaries
C
u
m
u
la
tiv
e
F
r
e
q
u
e
n
c
y
The More than Ogive
0
10
20
30
40
50
60
14.5 24.5 34.5 44.5 54.5 64.5 74.5 84.5
Class Boundaries
Cumulative
Frequency

LINE GRAPH
Year 1986 1987 1988 1989 1991
Values 20 10 30 15 1
Example . Draw a line graph for the following time
series.
1986 1987 1988 1989 1990 1991
0
5
10
15
20
25
30
35
20
10
30
15
25
10
A line graph showing the above time
series
Year
Values

VERTICAL LINE GRAPH
• Is a graphical representation of discrete data and
frequencies.
• Vertical solid lines are used to indicate the
frequencies.
• Example . Draw a vertical line graph for the
following data
Family A B C D E
Number of children 2 1 5 4 3

BAR CHART (BAR DIAGRAM)
• Histogram, Frequency polygon, ogives are used
for data having an interval or ratio level of
measurement.
• Bar chart is a series of equally spaced bars of
uniform width where the height (length) of a
bar represents the frequency corresponding
with a category.
• Bars may be drawn horizontally or vertically.
Vertical bar graphs are preferred as they
allow comparison with other bars.
• Example: Revenue (in millions of Birr) of
company x from 1980 to 1982 is given below

1980 1981 1982
0
50
100
150
200
250
A simple bar chart showing
revenues of company X from
1980 to 1982
year
Revenue
Year Maize Wheat
1980 40 80
1981 20 60
1982 60 100
Year Revenue
1980 50
1981 150
1982 200
1980 1981 1982
0
10
20
30
40
50
60
70
80
90
100
40
20
60
80
60
100
The number of quintals(in
thousands) of wheat and maize
production
maize
wheat
Year
Number of
quintals

1980 1981 1982
0
100
200
300
400
500
600
150
300
350
150
200 100
The number of
quintals of wheat and
maize produced by
country X
Maize
Wheat
Year
Number
of
quintals
Example : percentage bar chart
Year % of Wheat Production % of Maize
Production
1980 150/300  100 = 50 150/300  100 = 50
1981 300/500  100 = 60 200/500  100 = 40
1982 350/450  100 = 78 100/450  100 = 22
1980 1981 1982
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
50
60
78
50
40
22
Percentage of wheat and maize
production from 1980-1982
wheat
maize
Year
Percentage
produced
SUBDIVIDED BAR CHART
Year Wheat Maize
1980 150 150
1981 300 200
1982 350 100

PIE CHART
• A pie chart is a circle that is divided in to sections or
according to the percentage of frequencies in each
category of the distribution.
• Example: The monthly expenditure of a certain family is
given below.
Items Expenditure % Proportion (Pfi) Degrees (360o
Rfi)
Clothing 100 100/1000  100 = 10 100/1000  360o
= 36
Food 350 350/1000  100 = 35 350/1000  360o
= 126
House Rent 250 250/1000  100 = 25 250/1000  360o
= 90
Miscellaneous 300 300/1000  100 = 30 300/1000  360o
= 108
Total 1000 100% 360o

350
250
100
300
Food House rent
Clothing Misc.
Solution: The pie chart for the above expenditure is
as follows

PICTOGRAPH (PICTOGRAM)
• A pictograph is a graph that uses symbols or pictures
to represent data.
• Example : In comparing the population of a country
from 1990 to 1992, we simply draw pictures of people
where each picture may represent 1000,000 people.
1992 -  Key:  = 1,000,000
1991 - 
1990 - 

chapter 2 data collection and presentation business statistics

chapter 2 data collection and presentation business statistics

Recommended

More Related Content

Similar to chapter 2 data collection and presentation business statistics (20)

Recently uploaded (20)

chapter 2 data collection and presentation business statistics