MBA Super Notes: Statistics: Data

MBA Super Notes© M S Ahluwalia Sirf Business
Version 1.0
Data

MBA SUPER NOTES
Statistics

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Data and its types
1

Data
5
1
Types of data
Primary and
Secondary
Qualitative and
Quantitative
Discrete and
Continuous
Nominal,
Ordinal, Interval
and Ratio
Cross-sectional,
Temporal and
Spatial
Variables • When we measure the attributes of an object, we obtain a value that varies
between objects.
• Example: consider the people in a class as objects and their height as the
attribute. The attribute height varies between objects, hence attributes are
collectively known as variables.
Data • Name for values of a variable under study, taken collectively
• Basic source for descriptive and inferential statistics
*Explained further in the following pages

Primary and secondary data
6
1
Primary data
• Collected for some specific purpose or
study
• Methods such as personal investigation
or questionnaire used
Secondary Data
• Has its roots in primary data
• Data disseminated through media like
reports and agencies
Same data may be Primary as well as secondary depending upon the frame of reference.
Example: For the person who collects data through surveys it is primary data. But once a report
containing the data is published, for anyone using the data from the report it would be
secondary.
Collection of primary data
• Personal investigation
• Questionnaire
• Step 1: Design questionnaire
• Step 2: Collect data by conducting
survey
Collection of secondary data
• Publications by governments, regulatory
bodies
• Publications by industry associations
• Research on the internet

Qualitative and quantitative data
7
1
Qualitative/Categorical data
• Characterized in terms of names or labels
• Nominal level data are also known as
Qualitative data
• Ex: variables with yes/no or male/female
as responses
Quantitative/Numerical data
• Characterized in terms of numeric values
• Ordinal, Interval and Ratio level data are
also collectively known as Quantitative
data
• Ex: variables such as height, income,
marks
Qualitative/categorical
Discrete
Nominal Ordinal
Quantitative/numerical
Discrete or continuous
Interval Ratio
Types of data

Discrete and continuous data
8
1
Discrete
• Arises when counting is involved
• Assumes only specified values in a given
range
• Ex: Number of fruits in a box
Continuous
• Arises when measurement is involved
• Variable assumes all possible values in
range
• Ex: Height

Nominal, ordinal, interval and ratio data
9
1
Nominal data
• Data are
measured at the
nominal level
when each case
is classified into
one of a number
of discrete
categories
• Ex: Colors, Roll
numbers, Subject
codes
Ordinal data
• Data are
measured on an
ordinal scale if
the categories
imply order
• Data that is
nominal and has
order
• The difference
between ranks is
consistent in
direction, but not
magnitude
• Ex: Military rank,
Hotel ratings
Interval data
• Quantitative data
that can be
measured on
numerical scale
• Zero point does
not mean the
absence of
something
• Ex: Temperature
Ratio data
• Quantitative data
that can be
measured on
numerical scale
• Zero point means
the absence of
what is being
measured
• This is the most
common scale of
measurement
• Ex: Height, sales

Cross-sectional, temporal and spatial
10
1
Cross-sectional data
• Values of a variable
recorded over at the
same point or period of
time for many subjects
• Ex: age of all students in
a particular year, stock
prices of a set of
companies in a given
year
Temporal/Time-series data
• Data about a subject
over a period of time
• Ex: Inflation of a country
in last 5 years, students
taking admission in last 3
years
Spatial data
• Data being viewed by
geography
• Ex: population of state
capitals, revenues of a
company across
geographies

Data presentation
2.2

Graphical descriptive statistics
12
2
Graphs in
statistics
• Graphs and to a lesser extent, tables, give a visual summary of a variable
• Ideally there is an indication of the central (or “average”) value of the variable
as well as an indication of the amount and pattern of variability (“spread”)
• The level of data restricts the type of graphs and/or tables that can be used

Classification and tabulation
13
2
Frequency distributions
Classification • Bringing together items that are similar in some respect
Tabulation • To condense the data in a tabular form to make it easier to comprehend
Frequency
distribution
• Tabular representation of the number of times an item occurs by grouping
them into numerically ordered categories
• Data recorded at either Ordinal, Interval or Ratio levels are summarized by
frequency distributions
• Some information is lost in the process of generating the distribution
• Number of intervals used is decided by the user
• Class width is determined after the number of intervals is decided upon
(preferably widths should be same)
• There should be no overlap
Relative
frequency
distribution
• Tabular representation of the proportion of times an item occurs

Stem and
leaf diagram
• Stem and Leaf plots are a useful way of ordering data so we can study their
characteristics. It simultaneously organizes the data for further analyses, and
presents the data in both table and chart form
• It is essentially an ordered array, frequency distribution and histogram all in
one
• The S & L display contains all the same information, but also allows us to
easily look at critical aspects of the data, such as where the highest and
lowest values are, where most of the values lie, where the middle of the
values is etc.
• The drawback can occasionally be with deciding stem values
• It is preferable to order the leaves, to make the representation more
insightful, though not necessary
Stem and leaf diagram
14
2
Sample stem and leaf diagram
Stem unit: 100
Corresponding values
(rounded off to nearest 10)
4 7 8 470, 478
5 1 1 5 5 9 510, 510, 550, 550, 590
6 2 3 5 7 8 9 620, 630, 650, 670, 680, 690
7 0 1 4 5 700, 710, 740, 750
8 5 7 9 850, 870, 890

Visual representation of frequency distributions (1/2)
15
2
Histograms
• A graphical
representation of the
frequency distribution
Frequency polygons
• The class frequencies are
plotted above the
midpoint of each class
interval and connected
by straight lines
• An alternative to the
histogram best suited for
comparing two or more
frequency distributions
• The frequency polygons
do not have the
restriction of limits
between 0 and 1
Ogive
• A graph of cumulative
relative frequency
distributions
• It has value = 0 at the
lower limit of first class
and value = 1 at the
upper limit of highest
class
• Used to predict the
approximate proportion
of observations more or
less than a given value
• Ex: # of calls < 60 sec
0
1
2
3
4
5
6
<20 20-40 40-60 >60
Numberofcalls(thousands)
Duration in seconds
Call duration
0
1
2
3
4
5
6
<20 20-40 40-60 >60
Numberofcalls(thousands)
Duration in seconds
Call duration
0.00
0.20
0.40
0.60
0.80
1.00
<20 20-40 40-60 >60
Numberofcalls
(ratiooftotal)
Duration in seconds
Call duration

Visual representation of frequency distributions (2/2)
16
2
Cross tabulation
• It summarizes
the data for two
variables
simultaneously
Line graph
• Visual
representation of
a set of data
joined by straight
lines
Lorenz curve
• It represents the
extent of
inequality in a
data-set
• Area between
the line of
perfect equality
and the line of
actual equity
holding indicates
departure from
equality
Scatter diagram
• Graphical
representation of
relationship
between two
quantitative
variables
0
2
4
6
8
Q1 Q2 Q3 Q4
Sales
Sales
0
0.5
1
1.5
2
2.5
3
3.5
0 1 2 3

Pie charts
• Graphical representation of the
proportion of times an item occurs
• A circle divided into a number of sectors
each representing relative magnitude of
various components
• Effective when the aim is to display the
relative size of the categories
Bar charts
• Graphical representation of the number
of times an item occurs
• The frequency for each category is
represented by a bar
• Can be raw or relative frequencies
• Bars are separated by spaces
Graphical representation of qualitative data
17
2
59%23%
10%
8%
Sales
1st Qtr
2nd Qtr
3rd Qtr
4th Qtr
0
1
2
3
4
5
6
7
Q1 Q2 Q3 Q4
Sales
Sales

Types of Bar charts
18
2
Component Bar
chart
• Also known as
grouped or
percentage bar
chart
• A rectangular
equivalent of a
pie chart (when
only one x axis
value)
• Used for
comparison of
percentage
composition
Subdivided bar
chart
• Each bar is
further divided
into components
Multiple bar chart
• Multiple bars for
each point of
series
Pareto chart
• Bars are arranged
in order of height
(frequency) from
largest to
smallest
• Facilitates
identification of
most frequent
occurrence or
causes of an
event or
phenomenon
0%
20%
40%
60%
80%
100%
Q1 Q2 Q3 Q4
Sales
East
South
West
0
2
4
6
8
10
12
14
Q1 Q2 Q3 Q4
Sales
East
South
West
0
1
2
3
4
5
6
Q1 Q2 Q3 Q4
Sales
West
South
East
0
1
2
3
4
5
Q4 Q1 Q3 Q2
Sales
Sales

Do you have any questions
or some feedback to share?
Send an email to
super.msahluwalia@yahoo.com
Thank You!
19

M S Ahluwalia, is a top B-School graduate (MBA, Finance), CAIIB & JAIIB (both with ‘First class with
Distinction’) and ex-Banker from India.
He’s also a visual artist, blogger, designer and photographer. To know more please visit Estudiante De La
Vida or follow on Twitter or Facebook:
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MBA Super Notes: Statistics: Data

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