B. Com. -I Statistics Practical No. 1 Classification, tabulation and frequency distribution –I: Qualitative data.
Shree GaneshA
B. Com. Part – I: Semester – I
OE–I Semester
– I
(BASIC STATISTICS PRACTICAL-I)
Practical: 60 Hrs. Marks: 50 (Credits: 02)
Course Outcomes:
After completion of this practical course, the
student will be able to:
i) apply sampling techniques in real life.
ii) perform classification and tabulation of primary
data.
iii) represent the data by means of simple diagrams
and graphs.
iv) summarize data by computing measures of central
tendency.
LIST OF
PRACTICALS:
1. Classification, tabulation and frequency
distribution –I: Qualitative data.
2. Classification, tabulation and frequency
distribution –II : Quantitative
data.
3. Diagrammatic representation of data by using Pie
Diagram and Bar Diagrams.
4. Graphical representation of data by using Histogram,
Frequency Polygon, Frequency Curve and
Locating Modal Value.
5. Graphical representation of data by using Ogive
Curves and Locating Quartile Values.
6. Sampling : Simple random
sampling (with and without replacement) and stratified random sampling.
7. Measures of central tendencies: Mean, Mode and
Median.
8. Case study : Application of at least three practical’s
from above.
Note: Essential requirements for doing all the practical’s
from above list are:
i) Students should be made familiar with theory part
of every practical.
ii) Students are expected to be familiar in using
MS-Excel software as an essential computing tool,
otherwise they also can use Scientific Calculators.
Reference Books:
1. Agarwal B. L. (2019) Basic Statistics, New Age
International (P) Limited.
2. Gupta S. C. (2019) Fundamentals of Statistics,
Himalaya Publishing House Pvt. Ltd.
3. Patil P.Y. and Kore B. G. (2023) Statistics
Practical Paper–I, Nirali Publication, Kolhapur
4. Rita Kumari (2023) Sankhiki: Statistics, Motilal
Banarasidas.
5. Sharma V. K. (2012) Elements of Statistics,
Gullybaba Publishing House Pvt. Ltd
Classification,
tabulation and frequency distribution –I: Qualitative data.
1. Classification,
tabulation and frequency distribution.
In this section we study the following
points:
i.
Classification and it Bases.
ii.
Tabulation.
iii. Frequency
and Frequency Distribution.
I. Classification and it's Bases:
Classification:- The
process of arranging data into different classes or groups according to their
common characteristics is called classification. e.g. we dividing
students information into age, gender
and religion.
Or
Classification is a method used to categorize data into
different groups based on the values of specific variable. The purpose of
classification is to condenses the data, simplifies complexities, it useful to
comparison and helps to analysis.
The following are some criteria to classify the data into
groups.
i. Quantitative
Classification: - Quantitative classification deals with data consist
of numerical value and it can divided into two types as a) Discrete variable
and b) Continuous Variable
a) Discrete Variable:
- Discrete Variable take only the specific values, like integer values only.
For example the number of children's in a family, the numbers of cars in
parking lot etc.
b) Continuous Variable:-
Continuous variable takes any value in the range, or it measure on continuous
scale. For example age, height, weight, temperature etc.
ii. Qualitative
Classification:- it is also known as categorical or nominal classification,
this type of classification is used when data is divided into different groups
or categories. Without any numerical value. For example we classify the
data into gender ( male and female), according to car brand( Toyota, Ford,
Suzuki) etc.
iii. Chronological
Classification :- The data are arranged according to time is called
Chronological Classification, or data based in time order. This type of data
are used in time series analysis. In this type data are recorded or collected
in regular in time interval. For example daily sale data, daily price of
gold, record of daily temperature etc.
iv. Geographical
Classification:- The process of dividing data based on their geographical
location. Or the data collected based on different locations then it is called
geographical data. And this data is divided according to geographical location
is called geographical Classification. For example we collecting data of
population indifferent states, sales data collected form different city's.
etc.
II.TABULATION:- Tabulation is a next step of the Classification.
It is defined as the process of arranging data into row and column. The purpose
of the Tabulation is same as the Classification.
The following are parts of table:-
1. Table number
2. Title of table, Head-Note
3. Caption
4. Stub
5. Body of the table
6. Source note, foot note.
We see as:
1. Table Number: - Each
table should be give number. It is helpful to give reference in any
chapter.
2. Title of the table and Head
note: - Each table should be give a short and clear title. The purpose
of title describe the about data. A Head note is give information about data,
and its units.
3. Caption: - Caption
means heading of the column. If more columns in table we give sub-headings.
4. Stub: Stub refers to
the heading of the row and they give at the extreme left.
5. Body of the table: Body
is the main part of the table, data are given in the numerical form.
6. Source note and foot note: -
If data are taken from the other sources it can be mentioned in this note is
Sources note. And foot note provide the additional information or explanation
about data presented in table.
This part is shown in following table.
Table Number:
Title:
(Head Note if any)
|
|
Caption ( column heading) |
Total (Row) |
|||
|
Sub - Heading |
Sub - Heading |
||||
|
Stub (row heading) |
|
|
|
||
|
Column Total |
|
|
|
||
Source Note:
(Foot Note: if any )
Types of table:
There two types
of table based on the number of characteristics shown in the table.
i. Simple and
ii. Complex tables.
The classification of the tables are based on the number of
characteristics shown in the table. We consider one variable two divided
data into two parts is called simple table or one-way table. (Because
here consider one variable or attribute). Otherwise complex table i.e. we table
shown the more than two variable mean data divided into four parts is called
complex table.
We see the example of simple table and complex table.
i. Simple
table: in this case
we shown one variable that divide data into two part, e.g. the age of students
in a certain college there the table contain two column as name of the student
and their age. Here we are interested in the age of the students only.
|
Students Name |
Age |
|
Student1 |
20 |
|
Student2 |
18 |
|
Student3 |
19 |
|
Student4 |
21 |
This is an example of simple table.
ii. Complex
table:
Two –way table: collect the data of number of persons arrival at college
collecting data with arrival time and gender.
|
Arrival time |
Number of persons |
|
|
|
M |
F |
|
07:00 AM TO 08:00 A.M. |
14 |
12 |
|
08:00 A.M. TO 09:00 A.M. |
102 |
105 |
|
09:00A.M. TO 10:00 A.M. |
50 |
45 |
Now we colleting dada according to arrival time,
gender and the number of persons can divided into students and college staff.
|
Arrival time |
Number of persons |
|||
|
|
Students |
College staff |
||
|
|
M |
F |
M |
F |
|
07:00 AM TO 08:00 A.M. |
17 |
5 |
1 |
4 |
|
08:00 A.M. TO 09:00 A.M. |
34 |
36 |
14 |
5 |
|
09:00A.M. TO 10:00 A.M. |
10 |
7 |
4 |
5 |
It is an another example of complex table.
IV. FREQUENCY AND FREQUENCY DISTRIBUTION
Frequency: The number of times the particular Category repeated
in data set is called Frequency of that Category. it is
denoted as later f.
A frequency distribution of qualitative data is a table
that shows how many times each category appears or repeated in a data set. For
Example. Following data gives favorite type of fruit of 10 students. As apple,
bananas, grapes, mangoes, mangoes, apple, bananas, apple, grapes, grapes.
The frequency distribution for above data is:
In a data of favorite fruit of student apple,
bananas, grapes, mangoes only four fruit types are appears in data set.
Therefore we construct frequency distribution of that four fruits only.
|
Fruit |
Tally marks |
Frequency |
|
Apple |
III |
3 |
|
Bananas |
II |
2 |
|
Mangoes |
II |
2 |
|
Grapes |
III |
3 |
Here tally mark used for simple to
count the number of times repeat the particular fruit in given data.
A frequency
table shows each category and its corresponding frequency, representing how
often each category occurs in the dataset. This is known as a frequency
distribution.
Procedure for constructing a frequency distribution for Qualitative data.
The constructing a frequency
distribution for qualitative (or categorical ) data involves organizing the
data into a table that shows the number of times each category occurs.
The step by step Procedure
Step1 :Write all given
Qualitative data
First write a all qualitative data or given data ( categories).
Step2 : Identify
Unique Categories.
Write all unique categories present in a given data.
Step 3: Count the
Frequency for each category
Count
how many times each category appears in the data. We also use tally marks for initial
count and then convert them to numbers we get frequencies for each category.
Step 4 : Create a
frequency table.
Make a table for categories and corresponding
frequencies.
Example: Construct
a frequency distribution for following data.
Car, Bike, Car, Bus, Bike, Car, Bus, Bike, Car, Bus, Bus, Bike.
Answer: Constructing a frequency distribution for above
data First write a all given data as
Car, Bike, Car, Bus, Bike, Car, Bus, Bike, Car, Bus, Bike, Car, Bus, Bike,
Car.
Then the unique categories present in a given data are
car, bike, bus
Next Count the Frequency for each
category
|
Category |
Tally Mark |
Frequency |
|
Car |
IIII |
4 |
|
Bike |
IIII |
4 |
|
Bus |
IIII |
4 |
Therefore the frequency distribution of
given data is.
|
Category |
Frequency |
|
Car |
4 |
|
Bike |
4 |
|
Bus |
4 |
Practical Examples on
Shikshan Prasarak Santha’s
PADMABHUSHAN
VASANTRAODADA PATIL MAHAVIDHYALAYA
KAVATHE
MAHANKAL
DEPARTMENT
OF STATISTICS
B. Com.
I : Practical - I
Expt. No. 1
Date: / / 2024
Title: Classification, tabulation and frequency distribution: I.
Qualitative Data.
Q.1 The job grades (A, B, C, D
and E) of 40 employees are as follows:
|
A |
D |
B |
A |
A |
D |
E |
D |
E |
A |
|
B |
D |
A |
C |
C |
D |
E |
A |
B |
D |
|
C |
B |
A |
D |
E |
A |
E |
D |
B |
A |
|
D |
E |
D |
E |
A |
A |
D |
D |
B |
B |
Construct a frequency distribution
of these job grades.
Q.2 The Following are the blood groups of individuals. Construct a
frequency distribution for different blood groups.
|
A |
O |
B |
A |
AB |
B |
O |
B |
O |
A |
|
B |
B |
O |
O |
O |
A |
B |
AB |
A |
O |
|
B |
O |
AB |
AB |
B |
A |
AB |
B |
A |
O |
Q.3 Construct a frequency distribution for performance evaluation of
certain product.
|
High |
High |
Low |
High |
Average |
Low |
Average |
High |
|
Low |
Average |
High |
Low |
High |
High |
Low |
Low |
|
Average |
Average |
High |
Low |
Low |
High |
Low |
High |
Q.4 Construct a frequency distribution for weather conditions in July
2024.
|
Rainy |
Cloudy |
Sunny |
Cloudy |
Sunny |
Cloudy |
Rainy |
Rainy |
Sunny |
Sunny |
|
Cloudy |
Cloudy |
Rainy |
Sunny |
Rainy |
Sunny |
Rainy |
Cloudy |
Rainy |
Sunny |
|
Sunny |
Sunny |
Sunny |
Rainy |
Rainy |
Rainy |
Sunny |
Rainy |
Cloudy |
Rainy |
|
Rainy |
|
|
|
|
|
|
|
|
|
Q.5 Construct a frequency distribution for vehicle preference data of
20 persons.
|
Car |
Bus |
Bus |
Bike |
Car |
Bus |
Bus |
Bike |
Car |
Bus |
|
Bike |
Bike |
Car |
Bus |
Bus |
Bus |
Car |
Bus |
Bike |
Car |
|
|
|
|
|
|
|
|
|
|
|
Qualitative Frequency Distribution
Frequency Distribution
| Category | Frequency |
|---|
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