B. Com. I. Practical No. 2 : Classification, tabulation and frequency distribution –II. Quantitative 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 –II : Quantitative 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 data into age, gender and religion. It is an example of classification of student’s data 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)	Body
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.

III. Some Important Concepts:

        i. Constant:-   A measureable characteristic which does not change it's value is called Constant. e.g. area of earth. area of room.

      ii. Variable: A measureable characteristics which change it's value is called Variable. e.g. age, height.

       iii. Class limit: the lowest and highest value of the class are called Class Limits. e.g. in above example the 0-10 is a class it has to values as 0 and 10 that are the lower and upper limit of that class that are the class limit of that class, 10-20 that class has 10 and 20 are the class limits.

       iv. Class Width:  Class width is the difference between upper limit and Lower limit of class. and it is denoted as C. it is formulated as C= Upper limit - Lower limit.

        v. Frequency: Number of time particular value of the variable is repeated in data is called Frequency. and it is denoted as f.

        vi. Mid-Point:- The mid-point of class is  defined as average of lower and upper limit. 

i.e. mid-point = [lower limit + upper limit]/2.

        vii. Frequency density  of class interval :- frequency density of class interval is defined as the ratio of class frequency to the class width.  i.e. Frequency density = f/c, where f- frequency and c- class width.

        viii. methods of classification: a) Inclusive method, and b) Exclusive Method

                a) Inclusive Method : In this method the classes are formed that both limits, upper and lower limit included in same class.

                 b) Exclusive Method: In this method the class are formed as the upper limit of class is lower limit of next class. therefore the upper limit is not included in that class. e.g. if the classes are 0-10, 10-20 then that value 10 in data is not included in first class we include the value 10 in  second class 10-20.

        ix. Principles of frequency distribution: 

            a) Number of classes (k) : the number of classes are formed depends on the values in data set it is obtained as k= 1+3.322 x log(N)

where k is the number of classes and N be the population size.

            b) Class width (c): the size of class depends on number of classes and range of the data. it is calculated as  class width = c= (L-S) / K

where L - S = R = Range =(largest - smallest observation in data set.)

        Note that : if the class which has no lower limit of first class or no upper limit of last class, is called Open end classes.

        x) Relative Frequency : Relative Frequency is defined as ratio of class frequency and total frequency, Relative Frequency = f / N.

IV. FREQUENCY AND FREQUENCY DISTRIBUTION

The statistical table which shows the values of the variable arranged in order of magnitude of in group with respective frequencies side by side is called frequency distribution. or the way in which observation are distributed into various classes is called frequency distribution.

Frequency: The number of times the particular value of the variable repeated in data set is called Frequency of value. it is denoted as later f.

The way in which the value of variable is distributed into different classes is called frequency distribution. And the table in which the value of variable and their frequency are shown is called frequency distribution table or simply frequency distribution.

we study the following points as i. Un-Grouped Frequency Distribution, 

                                                    ii. Grouped Frequency Distribution. 

                                                    iii. Cumulative Frequency Distribution.

     i. Un-Grouped Frequency Distribution (Discrete frequency distribution) :- a frequency distribution in which different  values of the variable along with their frequency are shown is called Un-Grouped Frequency Distribution.

the formation of the Un-Grouped Frequency Distribution  we count the number of times particular value is repeated in data, that count is frequency of that variable.

Procedure for construction of  Un-Grouped Frequency Distribution (or Discrete frequency distribution)

Step I: First Arrange Data in ascending order.

Step II: Constructing a blank Table with three columns are Values of Variable, Tally Mark and Frequency

Step III: Read the observations one by one and assign the tally mark for each observation. In tally mark the fifth frequency is denoted by  cutting first four tally mark from top Right  to bottom Left and sixth frequency is again by straight tally mark.

Step IV: Count the tally marks of each observation and write the frequency for each observation. And write their number in frequency column.

We get the Un-Grouped Frequency Distribution

 

 

 

e.g. consider a following data to prepare discrete frequency distribution.

 7, 4, 5, 8, 1, 1, 4, 5, 8, 10, 4, 2, 7, 7, 8, 4, 5, 1, 6, 7, 5, 1, 2.

Answer: the discrete frequency distribution for given data is.

First we data in ascending order as 1,1,1,1,2,2,4,4,4,4,5,5,5,5,6,7,7,7,7,8,8,8,10

Values	Tally Mark	Frequency
1	IIII	4
2	II	2
4	IIII	4
5	IIII	4
6	I	1
7	IIII	4
8	III	3
10	I	1

   Note: by using COUNTIF() FUNCTION IN MS-Excel we obtain its discrete frequency distribution of variable.

ii. Grouped Frequency Distribution (Continuous frequency distribution):- a frequency distribution in which different classes of the variable with corresponding their frequencies are shown in table is called Grouped Frequency Table.

For Prepare grouped frequency distribution we count the number of observations fall into each class. and this count (or number) is frequency of that class.

Procedure for construction of  Grouped Frequency Distribution (Continuous frequency distribution):- 

Step I: First Arrange Data in ascending order.

Step II: Find Range                                                                                                                                       Range = Maximum value in data set – Minimum value in data set

Step III: For constructing grouped frequency distribution we decide the number of classes and class interval.                                                                                                       For decide number of classes as Number of Classes (K)  = 1+3.322 log₁₀(N)                        where N is the total number of data point or observations in data set.                    And round the value of K i.e. number of classes.

Class interval: the class interval is calculated by dividing the Range by number of classes.       Class Interval =( Range) / (Number of Classes).

Step IV: Classify the data by exclusive or inclusive method for calculated class interval

Step V: Constructing a blank Table with three columns are Classes for Variable, Tally Mark and Frequency.

Step VI: Read the observations one by one and assign the tally mark for each observation with corresponding class.

Step VII: Count the tally marks of each class and write the frequency for each class.

We get the Continuous frequency distribution

e.g. Construct a suitable frequency distribution, for the following data. With class limits 0-10, 10-20………90-100.

70, 45, 55, 18, 17, 07, 6, 84, 57, 23, 26, 98, 02, 11, 37, 58, 66, 77, 82, 87,  86, 37, 26, 15, 45, 78, 98, 71, 72, 57, 64, 24, 92, 48, 48, 35, 62, 68.

Answer: the Continuous frequency distribution for given data is

First we data in ascending order as 2, 6, 7,11 ,15, 17, 18, 23, 24, 26, 26, 35, 37, 37, 45, 45, 48, 48, 55, 57, 58, 59, 64, 62, 66, 68, 71, 72, 77, 78, 82, 84, 86, 87, 92, 98, 98.

Given class limits 0-10, 10-20 ,…..90-100

Class	Tally Mark	Frequency
0-10	III	3
10-20	IIII	4
20-30	IIII	4
30-40	III	3
40-50	IIII	4
50-60	IIII	4
60-70	IIII	4
70-80	IIII	4
80-90	IIII	4
90-100	III	3

 Note: By using MS-Excel we use the function =FREQUENCY ()  to obtain the frequencies of classes

    iii. Cumulative Frequency Distribution: 

the cumulative frequency is obtained as the frequency of first class is added to that of the second class, this sum is added to that of the third and so on then the frequency are obtained are called cumulative frequencies. and they are denoted as c.f.

there are two types of the cumulative frequencies i. less than and ii. greater than cumulative frequency. for calculating the less than cumulative frequency we add up the frequencies from above to bottom. we get less than cumulative frequency. for calculating  Grater Than Cumulative Frequency we add up the frequencies from bottom to top.

we see in the example both cumulative frequencies less than and grater than cumulative frequency. 

Marks	Frequency	Cumulative Frequency
		Less than	Greater than
0-10	1	1 (first frequency as it is 1)	71 (adding below sum 70 and class frequency 1,  70+1= 71)
10-20	7	8 (adding first and second frequency = 1+7=8)	70 (adding below sum 63, and class frequency7, 63+7 = 70)
20-30	26	34 (adding the above sum 8 and class frequency =  8+26=34)	63 (adding the last 37 and class frequency 26=26+37=63)
30-40	37	71 (adding the above sum 34 and class frequency 37=34+37=71)	37 ( last frequency as it is 37)

 

from this example we see how to find the cumulative frequencies.

 

 

 

B. Com. I : Practical - II

Expt. No. 2                                                                                      Date:    /    / 2024

Title: Classification, tabulation and frequency distribution –II : Quantitative data.

Q. 1. Obtain discrete frequency distribution, for the marks obtained by 24 students in an examination. 10, 25, 35, 20, 20, 30, 20, 40, 25, 30, 10, 15, 40, 20, 25, 25, 35, 30, 35, 15, 20, 25, 25, 20.

Q. 2. Obtain discrete frequency distribution for the following data on the word length for each of 50 words in a poem is shown below. 5, 4, 3, 5, 8, 6, 6, 3, 4, 3, 4, 4, 5, 2, 8, 6, 6, 7, 4, 5, 6, 4, 9, 6, 3, 4, 2, 2, 2, 9, 2, 3, 8, 2, 4, 7, 7, 2, 4, 4, 4, 3, 4, 4, 2, 4, 4, 9, 3, 7.

Q. 3. Obtain continuous frequency distribution by taking classes as 110-115, 115-120…. 135-140 for the following data. 127, 129, 131, 122, 124, 112, 114, 137, 114, 126, 129, 124, 126, 134, 128, 121, 129, 135, 118, 132, 127, 119, 133, 131, 125, 134, 117, 116, 131, 134.

Q. 4. Obtain continuous frequency distribution for the following data on marks obtained by 50 students in an examination. By taking classes as  10-20, 20-30, …..50-60.                      30, 45, 48, 55, 39, 55, 31, 12,18, 21, 54, 59, 51, 33, 43, 44, 10, 38, 19, 26, 41, 35, 37, 41, 46, 33, 51, 37, 58, 58, 17, 19, 23, 26, 29, 36, 57, 36, 35, 44, 43, 27, 19, 43, 22, 31, 47, 34, 31, 15.

Q. 5. Obtain discrete frequency distribution for the following data.                                                             1, 4, 5, 5, 4, 4, 1, 5, 4, 8, 6, 7, 6, 2, 5, 5, 1, 9, 3, 5, 10, 5, 1, 8, 8, 2, 4, 2, 8, 8, 5, 8, 1, 10, 7, 10, 6, 2, 3, 7, 7, 6, 3, 10, 1, 1, 2, 9, 7, 8, 9, 7, 6, 4, 6, 6, 5, 6, 7, 7.

Q. 6. Obtain the continuous frequency distribution by taking classes as 20-40, 40-60, ….160-180 for the following data obtained on variable x.                                                                            97, 105, 86, 100, 77, 130, 130, 57, 60, 115, 84, 115, 139, 90, 102, 93, 127, 83, 95, 110, 117, 137, 73, 129, 140, 105, 90, 70, 85, 61, 79, 88, 148, 114, 135, 84, 119, 100, 86, 86, 90, 59, 106, 154, 72, 80, 127, 86, 89, 85, 64, 55, 62, 91, 81, 110, 109, 130, 71, 22, 118, 94, 112, 145, 116, 149, 62, 131, 115, 75, 112, 65, 180, 88, 90, 89, 126, 119, 116, 70

 

***

Q. 1. Obtain discrete frequency distribution, for the marks obtained by 24 students in an examination. 10, 25, 35, 20, 20, 30, 20, 40, 25, 30, 10, 15, 40, 20, 25, 25, 35, 30, 35, 15, 20, 25, 25, 20.

Aim:  To Obtain discrete frequency distribution for given data.

Procedure:

Let X – is marks obtained by students in examination.

Enter the given values in column of MS-Excel worksheet.

 By using COUNTIF() function of  MS-Excel , we get the frequencies for each value of x. to get the discrete frequency distribution of X.

Now, to obtain the frequency of “10” in given data, chose blank cell on sheet and use MS-Excel function COUNTIF() on formula bar as =COUNTIF(Select Entered data, “10”) and then press Enter we get the frequency of 10 in selected cell.

Repeat this process for each values in given data, like 15, 20, etc.

Construct  discrete frequency distribution table:                                                                                          create a column for each value of marks (x)                                                                                        create another column for their corresponding frequencies obtained by using COUNTIF() function.

We get  its discrete frequency distribution in tabulated below:

Marks	No. of Students
10	2
20	6
25	6
30	3
35	3
40	2

 

Result:  The discrete frequency distribution of student’s marks is

Marks	10	20	25	30	35	40
No. Of Students	2	6	6	3	3	2

 

Let see in MS-Excel

1. Enter the Given data in single column (e.g. Column A)

A1	Marks
A2	10
A3	25
A4	35
A5	20
A6	20
A7	30
A8	20
A9	40
A10	25
A11	30
A12	10
A13	15
A14	40
A15	20
A16	25
A17	25
A18	25
A19	30
A20	35
A21	15
A22	20
A23	25
A24	25
A25	20

(In above data 10, 20, 25, 30, 35, 40 values are repeated so we find Frequency of this number only.)

2. for frequency of values:  Enter the Numbers in Next column (B) you want to find frequency of that number.

B1	No. of Students
B2	10
B3	20
B4	25
B5	30
B6	35
B7	40

 

 3.Then use the COUNTIF() function to get Frequency of 10, 20, 25, 30, 35, 40     In COUNTIF() function as =COUNTIF(Range means select entered data in column A, Criteria means select values in column B for that value find frequency )

A	B	C	D
Marks	No. of Students	Frequency function	Frequency
10	10	=COUNTIF(A2:A25,B2)	2
25	20	=COUNTIF(A2:A25,B3)	6
35	25	=COUNTIF(A2:A25,B4)	6
20	30	=COUNTIF(A2:A25,B5)	3
20	35	=COUNTIF(A2:A25,B6)	3
30	40	=COUNTIF(A2:A25,B7)	2
20
40
25
30
10
15
40
20
25
25
25
30
35
15
20
25
25
20

 

Result:

The discrete frequency distribution of student’s marks is

Marks	10	20	25	30	35	40
No. Of Students	2	6	6	3	3	2

 

 

Q. 2. Obtain discrete frequency distribution for the following data on the word length for each of 50 words in a poem is shown below. 5, 4, 3, 5, 8, 6, 6, 3, 4, 3, 4, 4, 5, 2, 8, 6, 6, 7, 4, 5, 6, 4, 9, 6, 3, 4, 2, 2, 2, 9, 2, 3, 8, 2, 4, 7, 7, 2, 4, 4, 4, 3, 4, 4, 2, 4, 4, 9, 3, 7.

Aim:  To Obtain discrete frequency distribution for given data.

Procedure:

Let X – is word length for each of 50 words in a poem. (i.e. no. of letters in word)

Enter the given values of word length in column of MS-Excel worksheet.

 By using COUNTIF() function of MS-Excel , we get the frequencies for each value of x. to get the discrete frequency distribution of X.

Now, to obtain the frequency of “7” in given data, chose blank cell on sheet and use MS-Excel function COUNTIF() on formula bar as =COUNTIF(Select Entered data, “7”) and then press Enter we get the frequency of 7 in selected cell.

Repeat this process for other values in given data like 2,3,4,5,6,7,8,9.

Construct a discrete frequency distribution table:                                                                                          create a column for each value of word length (x)                                                                                          create another column for their corresponding frequencies obtained by using COUNTIF() function.

We get its discrete frequency distribution in tabulated below:

Word Length	Frequency
2	8
3	7
4	15
5	4
6	6
7	4
8	3
9	3

 

Result:

The discrete frequency distribution of given data is.

Word Length	2	3	4	5	6	7	8	9
Frequency	8	7	15	4	6	4	3	3

Q. 3. Obtain continuous frequency distribution by taking classes as 110-115, 115-120…. 135-140 for the following data. 127, 129, 131, 122, 124, 112, 114, 137, 114, 126, 129, 124, 126, 134, 128, 121, 129, 135, 118, 132, 127, 119, 133, 131, 125, 134, 117, 116, 131, 134.

 

Aim:  To Obtain continuous frequency distribution for given data.

Procedure :

 Enter given data or values in  column of MS-Excel worksheet.

By using FREQUENCY() function of MS-Excel , we get the frequencies for each classes. (classes are 110-115, 115-120, 120-125, 125-130, 130-135, 135-140) To obtaining the frequency of classes we add one more column as BINS Array ( Bins Array contain the upper limit of all classes.) i.e. 115, 120, 125, 130, 135, 140

To obtain frequency of above classes, select cells ( no. of cells are equal to number of classes or no. of bins) against bins array and then use Frequency function as =FREQUENCY(select entered data, Bins array) and press Ctrl ,Shift and Enter on key board  to get frequency of all classes at same time.

Result:

The continuous  frequency distribution of given data is.

Class	FREQUENCY
110-115	3
115-120	4
120-125	5
125-130	8
130-135	9
135-140	1

  

Let see in MS-Excel

1.     Enter the Given data in single column (e.g. Column A)

Entered data in Column A from A1 to A30

A	Values
A1	112
A2	114
A3	114
A4	116
A5	117
A6	118
A7	119
A8	121
A9	122
A10	124
A11	124
A12	125
A13	126
A14	126
A15	127
A16	127
A17	128
A18	129
A19	129
A20	129
A21	131
A22	131
A23	131
A24	132
A25	133
A26	134
A27	134
A28	134
A29	135
A30	137

(In above example the classes are give 110-115, 115-120…. 135-140 so we find frequency of this classes.)

Now we enter the bins array mean the upper limit of the each class. In next column as

Entered upper limit in column B from B2 to B6

B	Bins array
B1	115
B2	120
B3	125
B4	130
B5	135
B6	140

 

To obtain frequency of above classes, select cells ( no. of cells are equal to number of classes or no. of bins) against bins array and then use Frequency function as =FREQUENCY(select entered data, Bins array) and press Ctrl ,Shift and Enter on key board  to get frequency of all classes at same time.

A	B	C	D
Values	Bins array	FORMULA	FREQUENCY
112	115	=Frequency(A1:A30,B1:B6)	3
114	120		4
114	125		5
116	130		8
117	135		9
118	140		1
119
121
122
124
124
125
126
126
127
127
128
129
129
129
131
131
131
132
133
134
134
134
135
137

 

Result:

The continuous  frequency distribution of given data is.

Class	FREQUENCY
110-115	3
115-120	4
120-125	5
125-130	8
130-135	9
135-140	1

 

 

  

Q. 4. Obtain continuous frequency distribution for the following data on marks obtained by 50 students in an examination. By taking classes as  10-20, 20-30, …..50-60.                      30, 45, 48, 55, 39, 55, 31, 12,18, 21, 54, 59, 51, 33, 43, 44, 10, 38, 19, 26, 41, 35, 37, 41, 46, 33, 51, 37, 58, 58, 17, 19, 23, 26, 29, 36, 57, 36, 35, 44, 43, 27, 19, 43, 22, 31, 47, 34, 31, 15.

Aim:  To Obtain continuous frequency distribution for given data.

Procedure :

 Enter given data or values in  column of MS-Excel worksheet.

By using FREQUENCY() function of MS-Excel , we get the frequencies for each classes. (classes are10-20, 20-30, 30-40, 40-50, 50-60) To obtaining the frequency of classes we add one more column as BINS Array ( Bins Array contain the upper limit of all classes.) i.e.20, 30, 40, 50, 60.

To obtain frequency of above classes, select cells ( no. of cells are equal to number of classes or no. of bins) against bins array and then use Frequency function as =FREQUENCY(select entered data, Bins array) and press Ctrl ,Shift and Enter on key board  to get frequency of all classes at same time.

Result:

The continuous  frequency distribution of given data is.

Class	FREQUENCY
10-20	8
20-30	8
30-40	14
40-50	11
50-60	9

 

 Q. 5. Obtain discrete frequency distribution for the following data.                                                             1, 4, 5, 5, 4, 4, 1, 5, 4, 8, 6, 7, 6, 2, 5, 5, 1, 9, 3, 5, 10, 5, 1, 8, 8, 2, 4, 2, 8, 8, 5, 8, 1, 10, 7, 10, 6, 2, 3, 7, 7, 6, 3, 10, 1, 1, 2, 9, 7, 8, 9, 7, 6, 4, 6, 6, 5, 6, 7, 7.

Aim:  To Obtain discrete frequency distribution for given data.

Procedure:

Let X – is a given data set.

Enter the given values in column of MS-Excel worksheet.

 By using COUNTIF() function of  MS-Excel , we get the frequencies for each value of x. to get the discrete frequency distribution of X.

Now, to obtain the frequency of “1” in given data, chose blank cell on sheet and use MS-Excel function COUNTIF() on formula bar as =COUNTIF(Select Entered data, “1”) and then press Enter we get the frequency of 1  in selected cell.

Repeat this process for each values in given data, like 1,,2,3,4,5,6,7,8,9,10

Construct a discrete frequency distribution table:                                                                                          create a column for each value of (x)                                                                                       create another column for their corresponding frequencies obtained by using COUNTIF() function.

We get  its discrete frequency distribution in tabulated below:

X	Frequency
1	7
2	5
3	3
4	6
5	9
6	8
7	8
8	7
9	3
10	4

 

 

 

 

Q.6 Obtain the continuous frequency distribution by taking classes as 20-40, 40-60, ….160-180 for the following data obtained on variable x.                                                                            97, 105, 86, 100, 77, 130, 130, 57, 60, 115, 84, 115, 139, 90, 102, 93, 127, 83, 95, 110, 117, 137, 73, 129, 140, 105, 90, 70, 85, 61, 79, 88, 148, 114, 135, 84, 119, 100, 86, 86, 90, 59, 106, 154, 72, 80, 127, 86, 89, 85, 64, 55, 62, 91, 81, 110, 109, 130, 71, 22, 118, 94, 112, 145, 116, 149, 62, 131, 115, 75, 112, 65, 180, 88, 90, 89, 126, 119, 116, 70

Aim:  To Obtain continuous frequency distribution for given data.

Procedure :

 Enter given data or values in  column of MS-Excel worksheet.

By using FREQUENCY() function of MS-Excel , we get the frequencies for each classes. (classes are20-40, 40-60, 60-80, 80-100, 100-120, 120-140, 140-160, 160-180) To obtaining the frequency of classes we add one more column as BINS Array ( Bins Array contain the upper limit of all classes.) i.e. 40, 60, 80, 100, 120, 140, 160, 180.

 To obtain frequency of above classes, select cells ( no. of cells are equal to number of classes or no. of bins) against bins array and then use Frequency function as =FREQUENCY(select entered data, Bins array) and press Ctrl ,Shift and Enter on key board  to get frequency of all classes at same time.

Result:

The continuous  frequency distribution of given data is.

Class	FREQUENCY
20-40	1
40-60	4
60-80	14
80-100	25
100-120	19
120-140	12
140-160	4
160-180	1