1st PUC Statistics Question Bank Chapter 3 Classification and Tabulation

Karnataka 1st PUC Statistics Question Bank Chapter 3 Classification and Tabulation

1st PUC Statistics Classification and Tabulation Two Marks Questions and Answers

Question 1.
What is classification of the data?
Solution:
Classification is the process of arranging the data in to groups or classes according to common

Question 2.
What are the objectives of classification?
Solution:

• To reduce the size of the data
• To bring the similarities together.
• To enable further statistical analysis

Question 3.
What are the basis/types of classification?
Solution:

1. Chronological classification
2. Geographical classification
3. Qualitative classification
4. Quantitative classification.

Question 4.
Give the formula of Sturge’s to find the number of classes. Or Give the formula used to determine the number of classes.
Solution:
The numbers of classes are obtained using Sturges’s Rule: k = 1 + 3.22 log N;
N-number of items.

Question 5.
For what purpose is correction factor used in frequency distribution?
Solution:
To get a better continuity between the class interval of a frequency distribution exclusive class intervals are used, so, if the frequency distribution is in inclusive class intervals isconverted into exclusive class intervals using correction factor.

Question 6.
What are the guidelines of classification?
Solution:
following are some guidelines following while classification:

• The number of classes should generally between 4 and 15.
• Exclusive classes should be formed for better continuity between the class intervals.
• The width of the classes should be usually kept constant throughout the distribution.
• Avoid open-end classes.
• The classes should be arranged in ascending or descending order.
• The lower limit of the first class should be either ‘o’ or multiple of 5.

Question 7.
Define the term tabulation
Solution:
Tabulation is a systematic arrangement of the classified data in to columns and rows of a table

Question 8.
Mention the parts of a Table
Solution:
Table No., Title of the table, Headnote/Sub-title, Captions, Stubs, Body of the table, Footnote & Source.

Question 9.
What are the objects of Tabulation?
Solution:
The object/Purpose of tabulation are:-

• It simplifies the complex data
• To facilitate for comparison
• To give an identity to the data
• To reveals trend and patterns of the data

Question 10.
How the number of classes using Prof. H.A.Sturge’s?
Solution:
The number of classes are obtained using Sturges’s Rule: k = 1 + 3.22 Log N

Question 11.
What are inclusive & exclusive class intervals?
Solution:
If in a class, both lower and upper limits are included in the same class are inclusive class intervals, eg. 0-9, 10-19, 20-29…
If in a class, the lower limit is included in the same class but the upper limit is included in the next class are exclusive class intervals, eg. 0-10, 10-20, 20-30…

Question 12.
Define frequency distribution
Solution:
A systematic presentation of the values taken by a variable and the corresponding frequencies is called Frequency distribution.

Question 13.
What are Marginal and Conditional frequency distributions?
Solution:
If in a bivariate frequency distribution, if the distribution of only one variable is considered, the distribution is called marginal frequency distribution.
If in a bivariate frequency distribution, if the distribution of only one variable is formed subject to the condition of the other variable it is called conditional frequency distribution.

Question 14.
What is the tabulation of the data?
Solution:
Tabulation is a process of systematic arrangement of the classified data in rows and columns, in the form of a table.

Question 15.
What are the parts of a table?
Solution:
The parts of a table are: Table No., Title of the table, Headnote/Sub-title, Captions, Stubs, Body of the table, Footnote & Source

Question 16.
What is the purpose of ‘table number’ in tabulation?
Solution:
A number should be given to each and every table, in order to distinguish and also for easy reference.

Question 17.
What are captions and stubs of a table?
Solution:
Captions: Column headings are called captions. They explain what the column represents. Captions are always written in one or two words on the top of each column.
Stubs: Row headings are called Stubs. They explain what the row represents. Stubs are usually written in one or two words at the left extreme sid/of each row.

Question 18.
Solution:
It is a brief explanatory note or statement given just below the heading of the table put in a bracket. The statistical units of measurements, such as in ‘000s, Rs., Million tones, crores, Kgs., etc., are usually put in bracket.

Question 19.
What is indicated by source note of a table?
Solution:
Below foot note or below the table, source of the data may be mentioned for verification to the reader, regarding publications, organizations, pages, Journals etc,

1st PUC Statistics Classification and Tabulation Five Marks Questions and Answers

Question 1.
Explain chronological classification and geographical classification of data with examples.
Solution:
Temporal/Chronological classification: when the data enumerated over a different period of time, the type of classification is called chronological classification. The above type of classification is called as time series, e.g. Time series of the population, is listed in chronological order starting with the earliest period.
Table showing the population of India

Geographical classification :
In this type of classification the data are classified on the basis of geographical or locational or area wise differences between various items. Such as cities, districts, states etc. e.g., production of sugar in India may be presented state wise in the following manner:-
Table showing the production of sugar in India

Question 2.
Explain qualitative and quantitative classification with examples.
Solution:
Qualitative classification: Classification of the different units on the basis of qualitative characteristics (Called Attributes). Such as sex, literacy, employment etc.
e. g., the members of a club can be classified on the basis of sex wise distribution as follows:-
Table showing the sex distribution of members of a club

Quantitative classification: classification of the number of units on the basis of quantitative data, such as according to Height, weight, Wages, Age (years), Number of children, etc, Thus the groups of a student may be classified on their heights as follows:-
Table showing the heights of students

Online midpoint calculator and find the midpoint of aline segment joining two points using the midpoint calcultor in just one click.

Question 3.
Define the following terms :
i. Frequency, class frequency:
Solution:
Frequency refers to the number of times an observation repeated (f). The number of observations corresponding to a particular class is known as the class Frequency Class frequency is a positive integer including zero

ii. Class limits:
Solution:
Class limits- Lowest and the highest values that are taken to define the boundaries of the class are called class limits

iii. Range of the class: It is the difference between highest and lowest value in the data, i.e., Range = H.V. – L.V.

iv. Width of the class: The difference between the upper and lower limits of class called width of the class. It is denoted by c or i.
i/c = Upper limit(UL) – Lower limit(LL)

v. Class mid point
Solution:
The central value of a class called mid value/point; $$\mathrm{m} / \mathrm{x}=\frac{\mathrm{LL}+\mathrm{UL}}{2}$$

vi. Define Frequency Density:
Solution:
The frequency per unit of class interval is the frequency density.
i.e. frequency density = $$\frac{\text { Frequency the class }}{\text { width of the class }}=f / w$$

vii. Relative frequency:
Solution:
Relative frequency.. is the ratio of frequency of class to the total frequency of the distribution
Relative Frequency $$\frac{\mathrm{f}}{\mathrm{N}}$$

viii. Class interval-inclusive, exclusive and open-end classes:
Solution:
If in a class, lower as well as upper limits are included in the same class are called Inclusive class
e. g. 30-39,40-49….
If in a class, the lower limit is included in the same class and upper limit is included in the next class, such a class is called Exclusive class, eg. 30-40, 40-50…
If in a class, the lower and upper limits of the class is not specified are called open end classes” e.g. less than/below, or more than/ above 100

ix. Cumulative frequency- less than and more than cumulative frequency:
Solution:
The added up frequencies are called cumulative frequencies.
The number of observations with values less than upper limit is less than cumulative frequency. (l.c.f) i.e. Frequencies added from the top.
The number of observations with values more than lower class limit is more than cumulative frequency (m.c.f)

x. Correction factor:
Solution:
It is half of the difference between lower limit of a class and upper limit of the preceding class. Thus,
Solution:
Correction facctor (C.F) = $$\frac{\text { Lower limit of a class-Upper limit of the precending class }}{2}$$

xi. A Frequency distribution Discrete, Continuous, Bi-variate, Marginal
Solution:
A systematic presentation of the values taken by a variable and the corresponding frequencies is called frequency is called Frequency distribution.
While framing a frequency distribution, if class intervals are not considered, is called discrete frequency distribution.
1. Example:
The number of families according to number of children .

While framing a frequency distribution, if class intervals are considered, is called continuous frequency distribution.

2. Example:
The following table showing the weight (kgs.) of persons

A frequency distribution formed on the basis of two related variables is called bi-variate frequency distribution.
For example, we want to classify data relating to the Height and Weights of a group of individuals, Income and Expenditure of a group of individuals, Ages of Husbands and Wives, Ages of mothers and Number of children, etc .
In a Bivariate frequency distribution, the frequency distribution of only one of the variables is considered, it is marginal frequency distribution.

Question 4.
Mention/what are the rules/principles of formation of Frequency of distribution?
Solution:

1. The lower limit of the first class should be either 0 or a multiple of 5
2. Exclusive classes should be formed for better continuity
3. The number of classes should be generally between 4 & 15
4. The width of the classes should be kept constant throughout the distribution
5. Avoid open-end classes
6. The classes should be arranged in ascending or descending order.

Question 5.
Mention the rules/principles of the tabulation
Solution:

1. The size of the table should be according to the size of the paper
2. The stubs and captions should be arranged logically according to the alphabetical, Chronological, Geographical order and items to be arranged according to the size.
3. If desired to locate the particular quantity in the body of the table that should be showed by thick colored inks or shaded off.
4. The table should not be overloaded with number of characteristics, rather can be prepare another table.
5. The table should be complete in all respects by captions and stubs, titles heading and no cell is left blank if left do not put ‘o’ but give (—) dash marks or write N.A
6. Miscellaneous column can be provided for the data which do not fit to the data, such as Ratio, percentages.
7. Ditto ( “ ) marks should not be used, as they may confuse with the no. 11
9. Sources if provided regarding publications, organizations, pages, Journals etc.

Question 6.
The employees of a college can be classified on the basis of sex wise distribution as follows:-
Solution:
Table showing the sex distribution of employess of a college.

Question 7.
The Employees of a college can be classified according to their occupations as :
Solution:
Table-1
The blank table given below represents the number of employees with different occupation in a college

 Occupations Number of employees Teaching staff – clerks – Attenders – Security men – Total –

Question 8.
The employees of a commercial Bank can be classified according to their occupations and sex is :
Solution:
Table-2
The blank table given below represents the number of employees with different occupation and their sex in a commercial Bank

Question 9.
The employees of a college can be classified according to their occupations , sex and their marital status is :
Solution:
Table-3 : The blank table given below represents the number of employees with different occupation, sex and their marital status in a college

Question 10.
In a survey of 40 families in a certain locality, the number of children per family was recorded and the following data were obtained.

Represent the data in the form of a discrete frequency distribution.
Solution:
Frequency distribution of the number of children.

Question 11.
Prepare a frequency table from the following table regarding the number fatal accidents occurred in a day in Bangalore in June 2010.

Solution:
Frequency distribution of the number of children.

Question 12.
From the following paragraph prepare a discrete frequency table with the number of letters present in the words .
“Success in the examination confers no right to appointment unless government is satisfied, after such enquiry as may be deemed necessary that the candidate is suitable for appointment to the public service”
Solution:
The number of digits in the above statement: Highest digit = 11 and Lowest digit = 2
Frequency distribution of the number of letters in the words present in the statement

Question 13.
The following are the marks obtained by 50 college students in a certain test.

Take suitable width of the class interval marks using struge’s rule.
Solution:
Here, N= 50; Range = H.V.-L. V. = 49-12 = 37
The number classes as per Sturge’s rule are obtained as follows:
Number of class intervals (K) = 1 + 3.322 logN= 1 + 3.22 log 50 = 1 + (3.22 × 1.6990) = 6.47=7
classes (Approx.) Size/width of class intervals – e = $$\frac{\text { Range }}{\text { Number of class intervals }}=\frac{37}{7}$$
5.28 = 6 (Approx.)
The size/width of each class is 6 and there are 7 classes. Thus, the required continuous frequency distribution with exclusive class intervals width is prepared as :
Frequency distribution of marks of students

Question 14.
The following data gives ages of 32 individuals in a locality. Using Sturge’s rule form a frequency table with exclusive type of class intervals.

Solution:
Here N= 32; Range = H .V.- L.V. = 59- 01 = 58
The number classes as per Sturge’s rule are:
Number of class intervals (K) =1 + 3.22 logN = 1 + 3.22 log (32) = 1+(3.22 × 1.5051) = 5.85=6
classes (Approx.) Size/width of class intervals – e = $$\frac{\text { Range }}{\text { Number of class intervals }}=\frac{58}{6}$$ = 10
(approx). Teh size / width of each class is 10 and there are 6 classes.
Frequency distribution of marks of students

Question 15.
The following are the marks obtained by 50 students in statistics; prepare a frequency table with class intervals of 10 marks.

Solution:
Range: H.V-L.V = 93 – 23 = 70; take width as 10 marks, and then the number of classes will be: 70/10=7.
Frequency distribution of marks of students in statistics test

Question 16.
Prepare a bivariate frequency distribution of the marks in Accountancy & Statistics:

Solution:
Here the both variables are discrete in nature no need to prepare class interval.
Bi-variate frequency table showing Ages (years) of Mothers and Number of children

Question 17.
Below are the ages of husbands and wives prepare a bivariate frequency distribution with suitable width :

Here both are continuous variables form the class intervals as below :
Solution:
Ages of Husbands: Highest age = 47, Lowest age = 25, Difference = 22/(i)5width =5. classes. Ages of wife: Highest age = 47, Lowest age = 21, Difference = 26/(i)5width = 6 (Approx.) classes.
Let X and Y be the ages of Husbands and ages of Wives.

Question 18.
Below are given the marks obtained by a batch of 20 students in mathematics and statistics:

Solution:
Marks in Mathematics: Highest Marks = 72, Lowest marks = 25, Difference = 47/(i)l Owidth 5 = 5 (Approx.) classes.
Marks in statistics: Highest marks = 85, Lowest marks = 20, Difference = 65/(i)10width = 7 (Approx.) classes.
Let x and y be marks inmathematics and marks in statistics.

TABULATION

Question 19.
Give a general format of a table.
Solution:
General format of a table

Question 20.
What are the requisites of a good table? Or What are the General rules to the tabulation?
Solution:

• Size:- the size of the table should be according to the size of the paper with more rows than columns. Exchange of the data can be done by altering the column and rows. A sufficient space should be provided in a particular to enter any new or to alter any affected figures.
• Logical order:- The stubs and captions should be arranged logically according to the alphabetical, Chronological, Geographical order and items to be arranged according to the size.
• Identity:- If desired to locate the particular quantity in the body of the table that should be showed by thick colored inks or shaded off.
• The table should not be overloaded with number of characteristics, rather can be prepare another table.
• The table should be complete in all respects by captions and stubs, titles heading and no cell is left blank if left do not put ’o’ but give (—) dash marks or write N.A
• Miscellaneous column can be provided for the data which do not fit to the data, such as Radius, percentages.
• Ditto ( “ ) marks should not be used,as they may confuse with the number 11
• Footnote may contain about errors, omissions, remarks
• Sources if provided regarding publications, organizations pages Journals etc.

Question 21.
Elucidate the difference between classification and tabulation.
Solution:
Comparison between Classification and Tabulation:-
The following points may be given as comparison:

• Classification and Tabulation are not two distinct processes. Before tabulation, data are classified and then displayed under different columns and rows of a table.
• Classification is the process of arranging the data in to groups or classes according to common characteristics possessed by the items of the data;
Whereas Tabulation is a process of systematic arrangement of the classified data in rows and columns, in the form of a table.
• Table contains precise and accurate information, where as classification gives only a classified groups of data.
• Classification reduces the size of the data and brings the similarities together and tabulation facilitates comparison, reveal the trend and tendencies of the data.

Question 22.
In the college out of total of 1200 applications received for I puc admission, 450
were applied for science and 580 applied for commerce and remaining applied for
arts faculty. Tabulate the above information.
Solution:
Table 1
Table showing the distribution of applicants for I year puc to different faculties

Question 23.
In the college out of total of 1200 applications received for I puc admission 780 were boys. 450 were applied for science of which 300 were boys and 580 applied for commerce 250 were girls and remaining applied for arts faculty. Tabulate the above information.
Solution
Table 2
Table showing the sex-wise distribution of applicants for I year puc to different faculties

Question 24.
In a Sigma multinational accountant consultants there are 180 were accountants, 210 were article helpers, 300 were practitioner trainees. Of all the members 30% were women among accountants, 20% in Articles helpers and 15% among trainees. Tabulate the data.
Solution:
Table 3
Table represents the members of Sigma accountants according to cadre and sex

Footnote: * 180 × 30%= 54, 210 × 20% = 42

Question 25.
In a trip organized by a college there were 80 persons each of whom paid Rs.15.50 on an average? There were 60 students each of whom paid Rs.16. members of the teaching staff were charged at higher rate. The number of ser ants was 6 (all males) and they were not charged anything. The number of females was 20 percent of the total of which one was a lady staff member. Tabulate the information.
Solution:
Table 4
Table showing the contribution (in Rs.) details made by members of a college trip.

Question 26.
In a state, there are 30 Medical colleges, 10 Dental colleges and 50 Engineering colleges. Among the Medical colleges, 5 are government colleges, 10 are aided private colleges and remaining are the unaided private colleges. Of the unaided colleges, 5 colleges are run by minority institutions.
Among the Engineering colleges, 10 are government colleges, 20 are aided private colleges and the rest are unaided private colleges. Of the unaided colleges, 10 colleges are run by minority institutions.
Among the dental colleges, 2 are aided private colleges and the rest are the unaided private colleges of which one is run by a minority institutions.
Tabulate the above information.
Solution:
Table showing the Medical, Engineering and Dental colleges run by Government, Private Aided and Private Unaided colleges in a State

Question 27.
The number of cases filed, hearing made and disposed by different bench judges in a day at High court of Karnataka are as given:
(i) Criminal cases filed 12, hearings made in 8 cases and disposed 3,
(ii) Land dispute cases filed 18, hearings made in 12cases and disposed 5,
(iii) Government service cases filed 6, hearings made in 4 cases and disposed 3,
(iv) Cheating cases filed 15; hearing made in 12 cases and disposed 8.
Tabulate the above information.
Solution:
Table showing the different types of cases filed, heard and disposed in a day at High court of Karnataka

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