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- they give a short revision at the time of CA Foundation Statistics exam
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- BASIC INTRODUCTION OF STATISTICS
- DATA,COLLECTION OF DATA
- SCRUTINY OF DATA
CHAPTER 1 : STATISTICAL DESCRIPTION OF DATA
CONTENT
BASIC INTRODUCTION OF STATISTICS
DATA,COLLECTION OF DATA
SCRUTINY OF DATA
CLASSIFICATION OF DATA
PRESENTATION OF DATA
CLASSIFICATION OF DATA
MODE OF PRESENTATION OF DATA
STATISTICAL SERIES
FREQUENCY DISTRIBUTION
GRAPHICAL PRESENTATION OF FREQUENCY SERIES
MODULE QUESTIONS
Q.1. Which of the following statements is false?
(a) Statistics is derived from the Latin word ‘Status’
(b) Statistics is derived from the Italian word ‘Statista’
(c) Statistics is derived from the French word ‘Statistik’
(d) None of these.
Q.2. Statistics is defined in terms of numerical data in the
(a) Singular sense
(b) Plural sense
(c) Either (a) or (b)
(d) Both (a) and (b).
Q.3. Statistics is applied in
(a) Economics
(b) Business management
(c) Commerce and industry
(d) All these.
Q.4. Statistics is concerned with
(a) Qualitative information
(b) Quantitative information
(c) (a) or (b)
(d) Both (a) and (b).
Q.5. An attribute is
(a) A qualitative characteristic
(b) A quantitative characteristic
(c) A measurable characteristic
(d) All these.
Q.6. Annual income of a person is
(a) An attribute
(b) A discrete variable
(c) A continuous variable
(d) (b) or (c).
Q.7. Marks of a student is an example of
(a) An attribute
(b) A discrete variable
(c) A continuous variable
(d) None of these.
Q.8. Nationality of a student is
(a) An attribute
(b) A continuous variable
(c) A discrete variable
(d) (a) or (c).
Q.9. Drinking habit of a person is
(a) An attribute
(b) A variable
(c) A discrete variable
(d) A continuous variable.
Q.10. Age of a person is
(a) An attribute
(b) A discrete variable
(c) A continuous variable
(d) A variable.
Q.11. Data collected on religion from the census reports are
(a) Primary data
(b) Secondary data
(c) Sample data
(d) (a) or (b).
Q.12. The data collected on the height of a group of students after recording their heights with
a measuring tape are
(a) Primary data
(b) Secondary data
(c) Discrete data
(d) Continuous data.
Q.13. The primary data are collected by
(a) Interview method
(b) Observation method
(c) Questionnaire method
(d) All these.
Q.14. The quickest method to collect primary data is
(a) Personal interview
(b) Indirect interview
(c) Telephone interview
(d) By observation.
Q.15. The best method to collect data, in case of a natural calamity, is
(a) Personal interview
(b) Indirect interview
(c) Questionnaire method
(d) Direct observation method.
Q.16. In case of a rail accident, the appropriate method of data collection is by
(a) Personal interview
(b) Direct interview
(c) Indirect interview
(d) All these.
Q.17. Which method of data collection covers the widest area?
(a) Telephone interview method
(b) Mailed questionnaire method
(c) Direct interview method
(d) All these.
Q.18. The amount of non-responses is maximum in
(a) Mailed questionnaire method
(b) Interview method
(c) Observation method
(d) All these.
Q.19. Some important sources of secondary data are
(a) International and Government sources
(b) International and primary sources
(c) Private and primary sources
(d) Government sources.
Q.20. Internal consistency of the collected data can be checked when
(a) Internal data are given
(b) External data are given
(c) Two or more series are given
(d) A number of related series are given.
Q.21. The accuracy and consistency of data can be verified by
(a) Internal checking
(b) External checking
(c) Scrutiny
(d) Both (a) and (b).
Q.22. The number of errors in Statistics are
(a) one
(b) two
(c) three
(d) four
Q.23. The distribution of shares is an example of the frequency distribution of
(a) A discrete variable
(b) A continuous variable
(c) An attribute
(d) (a) or (c).
Q.24. The distribution of profits of a blue-chip company relates to
(a) Discrete variable
(b) Continuous variable
(c) Attributes
(d) (a) or (b).
ANSWERS
C
B
D
D
A
B
B
A
A
C
B
A
D
C
A
C
B
A
A
D
C
B
A
B
LAST YEARS EXAM QUESTIONS
Q. 1. Which of the following statements is true ?
(a) Statistics is derived from the French word ‘ Statistik’
(b) Statistics is derived from the Italian word ‘Statista’
(c) Statistics is derived from the latin word ‘statistique’
(d) none of these
Q. 2. Which of the following is statistical data?
(a) Ram is 50 year old
(b) Height of ram is 5’6 and of Shyam and Hari is ‘53” and 5’4” respectively
(c) Height of ram is 5’6” and weight is 90kg
(d) sale of A was more than B and C
Q. 3. Profits made by xyz bank in different years refer to
(a) An attribute
(b) A discrete variable
(c) A continuous variable
(d) none of these
Q. 4. Nationality of a person is
(a) Discrete variable
(b) An attribute
(c) Continuous variable
(d) none
Q.5. Data are said to be______ if the investigator himself is responsible for the collection of data.
(a) Primary data
(b) Secondary data
(c) Mixed of primary and secondary data
(d) None
Q.6. In indirect oral investigation
(a) Data is not capable of numerical expression
(b) Not possible or desirable to approach informant directly
(c) data is collected from the books
(d) None of these
Q.7. In collection of data which of the following interview methods:
(a) Personal interview method
(b) telephone interview method
(c) Published data
(d) (a) and (b)
Q.8. The quickest method to collect primary data is
(a) personal interview
(b) Indirect interview
(c) mailed questionnaire
(d) telephonic interview
Q.9. Some important sources of secondary data are _____ :
(a) international and government sources
(b) International and primary sources
(c) Private and primary sources
(d) Government sources
Q.10. The data obtained by the internet are
(a) primary data
(b) secondary data
(c) Both (a) and (b)
(d) None of these
Q.11. Data collected on religion from the census reports are:
(a) Primary data
(b) secondary data
(c) Sample data
(d) (a) or (b)
ANSWER
B
B
C
B
A
B
A
D
A
B
B
CLASSIFICATION OF DATA,MODE OF PRESENTATION OF DATA MODULE AND LAST YEAR EXAM QUESTIONS
MODULE QUESTIONS
Q.1. Classification is of
(a) four
(b) Three
(c) Two
(d) One
Q.2. The mode of presentation of data are
(a) Textual, tabulation and diagrammatic
(b) Tabular, internal and external
(c) Textual, tabular and internal
(d) Tabular, textual and external.
Q.3. A table has
(a) four
(b) two
(c) five
(d) none parts.
Q.4. For tabulation, ‘caption’ is
(a) The upper part of the table
(b) The lower part of the table
(c) The main part of the table
(d) The upper part of a table that describes the column and sub-column.
Q.5. ‘Stub’ of a table is the
(a) Left part of the table describing the columns
(b) Right part of the table describing the columns
(c) Right part of the table describing the rows
(d) Left part of the table describing the rows.
Q.6. The entire upper part of a table is known as
(a) Caption
(b) Stub
(c) Box head
(d) Body.
Q.7. The unit of measurement in tabulation is shown in
(a) Box head
(b) Body
(c) Caption
(d) Stub.
Q.8. In tabulation source of the data, if any, is shown in the
(a) Footnote
(b) Body
(c) Stub
(d) Caption.
Q.9. The best method of presentation of data is
(a) Textual
(b) Tabular
(c) Diagrammatic
(d) (b) and (c).
Q.10. The most accurate mode of data presentation is
(a) Diagrammatic method
(b) Tabulation
(c) Textual presentation
(d) None of these.
Q.11. Details are shown by
(a) Charts
(b) Tabular presentation
(c) both
(d) none
Q.12. Which of the following statements is untrue for tabulation?
(a) Statistical analysis of data requires tabulation
(b) It facilitates comparison between rows and not columns
(c) Complicated data can be presented
(d) Diagrammatic representation of data requires tabulation.
Q.13. In general the number of types of tabulation are
(a) two
(b) three
(c) one
(d) four
Q.14. Diagrammatic representation of data is done by
(a) Diagrams
(b) Charts
(c) Pictures
(d) All these.
Q.15. The most attractive method of data presentation is
(a) Tabular
(b) Textual
(c) Diagrammatic
(d) (a) or (b).
Q.16. Hidden trend, if any, in the data can be noticed in
(a) Textual presentation
(b) Tabulation
(c) Diagrammatic representation
(d) All these.
Q.17. Graph is a
(a) Line diagram
(b) Bar diagram
(c) Pie diagram
(d) Pictogram
Q.18. The relationship between two variables are shown in
(a) Pictogram
(b) Histogram
(c) Bar diagram
(d) Line diagram
Q.19. The chart that uses logarithm of the variable is known as
(a) Line chart
(b) Ratio chart
(c) Multiple line chart
(d) Component line chart.
Q.20. Multiple line chart is applied for
(a) Showing multiple charts
(b) Two or more related time series when the variables are expressed in the same unit
(c) Two or more related time series when the variables are expressed in different unit
(d) Multiple variations in the time series.
Q.21. Multiple axis line chart is considered when
(a) There is more than one time series
(b) The units of the variables are different
(c) (a) or (b)
(d) (a) and (b).
Q.22. Horizontal bar diagram is used for
(a) Qualitative data
(b) Data varying over time
(c) Data varying over space
(d) (a) or (c).
Q.23. Vertical bar diagram is applicable when
(a) The data are qualitative
(b) The data are quantitative
(c) When the data vary over time
(d) (a) or (c).
Q.24. Divided bar chart is considered for
(a) Comparing different components of a variable
(b) The relation of different components to the table
(c) (a) or (b)
(d) (a) and (b).
Q.25. In order to compare two or more related series, we consider
(a) Multiple bar chart
(b) Grouped bar chart
(c) (a) or (b)
(d) (a) and (b).
Q.26. Pie-diagram is used for
(a) Comparing different components and their relation to the total
(b) Representing qualitative data in a circle
(C) Representing quantitative data in circle
(d) (b) or (c).
ANSWERS
A
A
C
D
D
C
A
A
B
B
B
B
A
D
C
C
A
D
B
D
D
B
D
C
A
LAST YEAR EXAMS QUESTIONS
Q.1. Data are classified into male/ female and graduate/ non-graduate classes. This data
classification is
(a) Cardinal data
(b) Ordinal data
(c) Spatial series data
(d) Temporal data
Q.2. Classification is of ___ kinds
(a) Two
(b) Three
(c) One
(d) Four
Q.3. The chronological classification of data are classified on the basis of:
(a) Attributes
(b) Area
(c) Time
(d) Class interval
Q.4. 100 persons are classified into male/Female and graduate/ non- graduate classes. This data
classification is
(a) cardinal data
(b) ordinal data
(c) spatial series data
(d) temporal data
Q.5.The factor that can be used to tabulate the data are:
(a) Sex
(b) Region
(c) Time
(d) All of the above
Q.6. The primary rules that should be observed in classification
(i) as far as possible, the class should be of equal width
(ii) The classes should be exhaustive
(iii) The classes should be unambiguously defined
Then which of the following is correct
(a) only (i) and (ii)
(b) only (ii) and (iii)
(c) only (i) and (iii)
(d) all (i), (ii) and (iii)
Q.7. Mode of presentation data
(a) Textual presentation
(b) tabulation
(c) oral presentation
(d) (a) and (b)
Q.8. A table has _____ parts
(a) Four
(b) two
(c) Five
(d) None
Q.9. The column headings of a table are known as:
(a) Body
(b) Stub
(c) Box – head
(d) Caption
Q.10. In tabulation source of data if any is shown in the
(a) Stub
(b) body
(c) Caption
(d) Footnote
Q.11. Stub is the
(a) Left part of the table
(b) Right part of the table
(c) Largest part of the table
(d) Smallest part of the table
Q. 12. The chart that uses logarithm of variable is known as:
(a) Ratio chart
(b) line chart
(c) multiple line chart
(d) Component line chart
Q. 13. Divided bar chart is good for
(a) Comparing various components of a variable
(b) Relating the different components of the whole
(c) (a) & (b)
(d) (a) or (b)
Q. 14. In order to compare two or more related series, we consider
(a) Multiple bar chart
(b) Grouped bar chart
(c) (a) or (b)
(d) (a) and (b)
Q.15. The most appropriate diagram to represent the data relating to the monthly expenditure on
different items by a family
(a) Histogram
(b) Pie – diagram
(c) frequency polygon
(d) Line graph
Q.16. The most appropriate diagram to represent the five – year plan outlay of india in different
economic sectors is
(a) Pie diagram
(b) Histogram
(c) Line – graph
(d) Frequency polygon
Q.17.Pie diagram is used for:
(a) Comparing different components and their relation to the total
(b) Representing quantitative data in circle
(c) Representing date in a circle
(d) Either (b ) or (c)
Q.18. Pie – diagram is used for
(a) Representing quantitative data
(b) Representing quantitative data
(c) Comparing different components and their relation to the total
(d) Both(a) and (b)
Q.19.Which of the following diagrams is appropriate to represent the various heads is total cost?
(a) Bar graph
(b) pie- chart
(c) multiple line chart
(d) scatter plot
Q.20. A suitable graph for representing the portioning of total into sub parts in statistics is
(a) A pictograph
(b) A Pie chart
(c) An ogive
(d) Histogram
Q.21. Circular diagram is always
(a) One – dimensional
(b) Two – dimensional
(c) Three – dimensional
(d) Cartograms
Q.22. Which of the following is not a two-dimensional figure?
(a) Line diagram
(b) Pie diagram
(c) Square diagram
(d) Rectangle diagram
Q.23. Arrange the dimensions of bar diagram, cube diagram and pie diagram in sequence
(a) 1,3,2.
(b) 2,1,3
(c) 2, 3, 1
(d) 3, 2, 1
Q.24. Arrange the following dimension wise: pie – diagram, bar diagram and cubic diagram
(a) 1,2,3
(b) 3,1,2
(c) 3,2,1
(d) 2,1,3
Q. 25. Which of the following is not a two-dimensional diagram?
(a) Square diagram
(b) Line diagram
(c) Rectangular diagram
(d) Pie – chart
Q. 26. If the fluctuations in the observed value are very small as compared to the size of the item, it
is presented by :
(a) Z chart
(b) Ogive curve
(c) False base line
(d) control chart
ANSWERS
B
D
C
B
D
B
D
C
D
D
A
A
C
C
B
A
A
C
B
B
B
A
A
D
B
C
STATISTICAL SERIES MODULE AND LAST YEAR EXAM QUESTIONS
MODULE QUESTIONS
Q.1. A frequency distribution
(a) Arranges observations in an increasing order
(b) Arranges observation in terms of a number of groups
(c) Relaters to a measurable characteristic
(d) all these.
Q.2 The frequency distribution of a continuous variable is known as
(a) Grouped frequency distribution
(b) Simple frequency distribution
(c) (a) or (b)
(d) (a) and (b).
Q.3. Mutually exclusive classification
(a) Excludes both the class limits
(b) Excludes the upper class limit but includes the lower class limit
(c) Includes the upper class limit but excludes the upper class limit
(d) Either (b) or (c).
Q.4. Mutually inclusive classification is usually meant for
(a) A discrete variable
(b) A continuous variable
(c) An attribute
(d) All of these.
Q.5. Mutually exclusive classification is usually meant for
(a) A discrete variable
(b) A continuous variable
(c) An attribute
(d) Any of these.
ANSWERS
D
A
B
A
B
LAST YEAR EXAMS QUESTIONS
Q.1. Sales of XYZ Ltd. For 4 months is
Months : Jan Feb. March Apr.
Sales : 10000 15000 18000 9000
The above data represents
(a) Discrete
(b) Continuous
(c) individual
(d) None of these
Q.2. The following frequency distribution
X 12 17 24 36 45
F 2 5 3 8 9
Is classified as:
(a) Discrete distribution
(b) Continuous distribution
(c) Cumulative frequency distribution
(d) None of the above
Q.3. What is an exclusive series?
(a) In which both upper and lower limit are not included in class frequency
(b) In which lower limit is not included in class frequency
(c) In which upper limit is not included in class frequency
(d) None of the above
ANSWERS
C
A
C
CUMULATIVE FREQUENCY DISTRIBUTION MODULE AND OBJECTIVE QUESTIONS
MODULE QUESTIONS
Q.1. Cumulative Frequency Distribution is a
(a) graph
(b) frequency
(c) Statistical Table
(d) distribution
Q.2. To find the number of observations less than any given value
(a) Single frequency distribution
(b) Grouped frequency distribution
(c) Cumulative frequency distribution
(d) None is used.
Q.3. The number of types of cumulative frequency is
(a) one
(b) two
(c) three
(d) four
Q.4. “Cumulative Frequency” only refers to the
(a) less-than type
(b) more-than type
(c) both
(d) none
Q.5. Class: 0—10 10—20 20—30 30—40 40—50
Frequency: 5 8 5 6 4
For the class 20—30, cumulative frequency is
(a) 20
(b) 13
(c) 15
(d) 28
Q.6. Out of 1000 persons, 25 per cent were industrial workers and the rest were agricultural
workers. 300 people enjoyed world cup matches on TV. 30 percent of the people who
had not watched world cup matches with industrial workers. What is the number of
agricultural workers who had enjoyed world cup matches on TV?
(a) 260
(b) 240
(c) 230
(d) 250
Q.7.A sample study of the people of an area revealed that total number of women were 40% and the
percentage of coffee drinkers were 45 as a whole and the percentage of male
coffee drinkers were 20. What was the percentage of female non-coffee drinkers?
(a) 10
(b) 15
(c) 18
(d) 20
Q.8. Cost of sugar in a month under the heads Raw Materials, labour, direct production and
others were 12, 20, 35 and 23 units respectively. What is the difference between the central
angles for the largest and smallest components of the cost of sugar?
(a) 72o
(b) 48o
(c) 56o
(d) 92o
Q.9. The number of accidents for seven days in a locality are given below :
No. of accidents : 0 1 2 3 4 5 6
Frequency : 15 19 22 31 9 3 2
What is the number of cases when 3 or less accidents occurred?
(a) 56
(b) 6
(c) 68
(d) 87
Q.10. The following data relate to the incomes of 86 persons :
Income in Rs. : 500–999 1000–1499 1500–1999 2000–2499
No. of persons : 15 28 36 7
What is the percentage of persons earning more than Rs. 1500?
(a) 50
(b) 45
(c) 40
(d) 60
Q.11. The following data relate to the marks of a group of students:
Marks : Below 10 Below 20 Below 30 Below 40 Below 50
No. of students : 15 38 65 84 100
How many students got marks of more than 30?
(a) 65
(b) 50
(c) 35
(d) 43
Q.12. Find the number of observations between 250 and 300 from the following data :
Value : More than 200 More than 250 More than 300 More than 350
No. of observations : 56 38 15 0
(a) 56
(b) 23
(c) 15
(d) 8
ANSWERS
C
C
B
A
C
A
B
D
D
A
C
B
LAST YEAR EXAMS QUESTIONS
Q.1. Out of 1000 persons, 25 per cent were industrial workers and the rest were agricultural workers
300 persons enjoyed world cup matches on T.V. 30 percent of the people who had not watched
world cup matches were industrial workers what is the number of agricultural workers who had
enjoyed world cup matches on TV?
(a) 230
(b) 250
(c) 240
(d) 260
Q.2. In 2000 out of a total of 1750 workers of a factory 1200 were members of a trade union. The
the number of women employed was 200 of which 175 did not belong to a trade union. In 2004 there
were 1800 employees who belonged to a trade union and 50 who did not belong to trade unions. Out of
all the employees in 2004 300 were women of whom only 8 did not belong to the trade union. On
the basis of this information the ratio of female members of the trade union in 2000 and 2004 is:
(a) 292 : 25
(b) 8 : 175
(c) 175 : 8
(d) 25 : 292
Q.3. There were 200 employees in an office in which 150 were married total male employees were
160 out of which 120 were married. What was the number of female unmarried?
(a) 30
(b) 10
(c) 40
(d) 50
Q.4. Cost of sugar in a month under the heads raw materials labour, direct production and other were
12 , 20 , 35 and 23 units respectively. What is the difference between the central angles for the
largest and smallest components of the cost of sugar?
(a) 720
(b) 480
(c) 560
(d) 920
Q.5. A pie diagram is used to represent the following data :
Source : Customs Excise Income tax Wealth tax
Revenue in million rupees: 120 180 240 180
The central angles in the pie diagram corresponding to wealth tax and income tax respectively:
(a) (1200, 900)
(b) (900, 1200)
(c) (600,1200)
(d) (900, 600)
Q.6. The following data related to the incomes of 90 persons :
Income in Rs. : 1500-1999 2000-2499 2500-2999 3000-3499
No. of persons : 13 32 20 25
What is the percentage of persons earning more than Rs. 2500 ?
(a) 45
(b) 50
(c) 52
(d) 55
Q.7. Find the number of observations between 350 and 400 form the following
Value : more than 300 more than 350 more than 400 more than 450
No. of observations : 48 25 12 0
(a) 13
(b) 15
(c) 17
(d) 19
Q.8. The frequency of class 20-30 in the following data is
Class : 0-10 10-20 20-30 30-40 40-50
Cumulative frequency : 5 13 28 34 38
(a) 5 (b) 28 (c) 15 (d) 13
Q.9. The data given below refers to the marks gained by a group of students :
Marks : below 10 below 20 below 30 below 40 below 50
No. of students : 15 38 65 84 100
Then the no of students getting marks more than 30 would be ____.
(a) 50
(b) 53
(c) 35
(d) 62
Q.10. If class interval is 10 -14, 15-19, 20-24, then the first class is
(a) 10 – 15
(b) 9.5 – 14.5
(c) 10.5 – 15.5
(d) 9 – 15
Q.11. The following data relates to the marks of a group of student
Marks No. of student
More than 70% 07
More than 60% 18
More than 50% 40
More than 40% 60
More than 30% 75
More than 20% 100
How many students have got marks less than 50% ?
(a) 60
(b) 82
(c) 40
(d) 53
Q.12. The number of observations between 150 and 200based on the following data is
Value : More than 100 more than 150 more than 200 more than 250
No. of observation : 76 63 28 05
(a) 46
(b) 35
(c) 28
(d) 23
Q.13. The number of car accidents in seven days in a locality are given below
No. of accidents : 0 1 2 3 4 5 6 7
Frequency : 12 9 11 13 8 9 6 3
What will be the number of cases when 4 or more accidents occurred?
(a) 32
(b) 41
(c) 26
(d) 18
Q.14. Find the number of observation between 250 and 300 from the following data
Value more than : 200 250 300 350
No. of observation : 56 38 15 0
(a) 38
(b) 23
(c) 15
(d) None of these
Q.15. Class: 0—10 10—20 20—30 30—40 40—50
Frequency: 4 6 20 8 3
For the class 20—30, cumulative frequency is
(a) 26
(b) 10
(c) 41
(d) 30
ANSWERS
D
D
B
D
B
B
A
C
C
B
A
B
C
B
D
IMPORTANT CONCEPTS RELATED TO CONTINUOUS SERIES MODULE AND LAST YEAR EXAM QUESTIONS
MODULE QUESTIONS
Q.1. The LCB is
(a) An upper limit to LCL
(b) A lower limit to LCL
(c) (a) and (b)
(d) (a) or (b).
Q.2. The UCB is
(a) An upper limit to UCL
(b) A lower limit to LCL
(c) Both (a) and (b)
(d) (a) or (b).
Q.3. length of a class is
(a) The difference between the UCB and LCB of that class
(b) The difference between the UCL and LCL of that class
(c) (a) or (b)
(d) Both (a) and (b).
Q.4. For a particular class boundary, the less than cumulative frequency and more than
cumulative frequency added up to
(a) Total frequency
(b) Fifty per cent of the total frequency
(c) (a) or (b)
(d) None of these.
Q.5. Frequency density corresponding to a class interval is the ratio of
(a) Class frequency to the total frequency
(b) Class frequency to the class length
(c) Class length to the class frequency
(d) Class frequency to the cumulative frequency.
Q.6. Relative frequency for a particular class
(a) Lies between 0 and 1
(b) Lies between 0 and 1, both inclusive
(c) Lies between –1 and 0
(d) Lies between –1 to 1.
Q.7. The number of “Frequency distribution” is
(a) two
(b) one
(c) five
(d) four
Q.8. (Class frequency)/(Width of the class ) is defined as
(a) Frequency density
(b) Frequency distribution
(c) both
(d) none
Q.9. Tally marks determines
(a) class width
(b) class boundary
(c) class limit
(d) class frequency
Q.10. A representative value of the class interval for the calculation of mean, standard deviation,
mean deviation etc. is
(a) class interval
(b) class limit
(c) class mark
(d) none
Q.11. The number of observations falling within a class is called
(a) density
(b) frequency
(c) both
(d) none
Q.12. Classes with zero frequencies are called
(a) nil class
(b) empty class
(c) class
(d) none
Q.13. For determining the class frequencies it is necessary that these classes are
(a) mutually exclusive
(b) not mutually exclusive
(c) independent
(d) none
Q.14. Most extreme values which would ever be included in a class interval are called
(a) class limits
(b) class interval
(c) class boundaries
(d) none
Q.15. The value exactly at the middle of a class interval is called
(a) class mark
(b) mid value
(c) both
(d) none
Q.16. Difference between the lower and the upper-class boundaries is
(a) width
(b) size
(c) both
(d) none
Q.17. In the construction of a frequency distribution, it is generally preferable to have classes of
(a) equal width
(b) unequal width
(c) maximum
(d) none
Q.18. For the construction of a grouped frequency distribution
(a) class boundaries
(b) class limits
(c) both
(d) none are used.
Q.19. In all Statistical calculations and diagrams involving end points of classes
(a) class boundaries
(b) class value
(c) both
(d) none are used.
Q.20. Upper limit of any class is ________ from the lower limit of the next class
(a) same
(b) different
(c) both
(d) none
Q.21. Upper boundary of any class coincides with the Lower boundary of the next class.
(a) true
(b) false
(c) both
(d) none.
Q.22. Excepting the first and the last, all other class boundaries lie midway between the upper limit
of a class and the lower limit of the next higher class.
(a) true
(b) false
(c) both
(d) none
Q.23. The lower extreme point of a class is called
(a) lower class limit
(b) lower class boundary
(c) both
(d) none
Q.24. For the construction of grouped frequency distribution from ungrouped data we use
(a) class limits
(b) class boundaries
(c) class width
(d) none
Q.25. When one end of a class is not specified, the class is called
(a) closed- end class
(b) open- end class
(c) both
(d) none
Q.26. Class boundaries should be considered to be the real limits for the class interval.
(a) true
(b) false
(c) both
(d) none
Q.27. For overlapping class-intervals the class limit & class boundary are
(a) same
(b) not same
(c) zero
(d) none
Q.28. For the overlapping classes 0—10 , 10—20 , 20—30 etc. the class mark of the class 0—10 is
(a) 5
(b) 0
(c) 10
(d) none
Q.29. For the non-overlapping classes 0—19 , 20—39 , 40—59 the class mark of the class 0—19 is
(a) 0
(b) 19
(c) 9.5
(d) none
ANSWERS
B
A
A
A
B
A
A
A
D
C
B
B
A
C
C
C
A
B
A
B
A
A
B
A
B
A
A
A
C
LAST YEAR EXAMS QUESTIONS
Q.1. The lower-class boundary is:
(a) An upper limit to lower class limit
(b) A lower limit to lower class limit
(c) Both (a) & (b)
(d) None of these
Q.2. The difference between the upper and lower limit of a class is called ______.
(a) Class interval
(b) Mid value
(c) Class boundary
(d) Frequency
Q.3. Most extreme values which would ever be included in a class interval are called:
(a) Class interval
(b) Class limits
(c) class boundaries
(d) None of these
Q.4. Mid values are also called _____
(a) Lower limit
(b) Upper limit
(c) class Mark
(d) None
Q.5. Relative frequency for a particular class lies between:
(a) 0 and 1
(b) 0 and 1 both inclusive
(c) -1 and 0
(d) -1 and 1
Q.6. Frequency density can be termed as
(a) Class frequency to the cumulative frequency
(b) Class frequency to the total frequency
(c) Class frequency to the class length
(d) Class length to the class frequency
Q.7. Frequency density corresponding to a class interval is the ratio of
(a) Class frequency to the total frequency
(b) class frequency to the class length
(c) Class length to the class frequency
(d) Class frequency to the cumulative frequency
Q.8. __________Series is continuous
(a) Open ended
(b) Exclusive
(c) Close ended
(d) Unequal class interval
Q.9. The number of times a particular item occurs in a class interval is called its
(a) Mean
(b) Cumulative frequency
(c) Frequency
(d) None of the above
Q.10. From the following data find the number class intervals if class length is given as 5
73,72,65,41,54,80,50,46,49,53.
(a) 6
(b) 5
(c) 7
(d) 8
Q.11. For data on frequency distribution of weights:
70,73,49,57,56,44,56,71,65,62,60,50,55,49,63 and 45 If we assume class length as 5, the number of
class intervals would be
(a) 5
(b) 6
(c) 7
(d) 8
ANSWERS
B
A
C
C
A
C
B
B
C
D
B
GRAPHICAL PRESENTATION OF FREQUENCY SERIES MODULE AND LAST YEAR EXAM QUESTIONS
MODULE QUESTIONS
Q.1. Mode of a distribution can be obtained from
(a) Histogram
(b) Less than type ogives
(c) More than type ogives
(d) Frequency polygon.
Q.2. To find the mode graphically
(a) Ogive
(b) Frequency Polygon
(c) Histogram
(d) none may be used.
Q.3. An area diagram is
(a) Histogram
(b) Frequency Polygon
(c) Ogive
(d) none
Q.4. A comparison among the class frequencies is possible only in
(a) Frequency polygon
(b) Histogram
(c) Orgies
(d) (a) or (b)
Q.5. The most common form of diagrammatic representation of a grouped frequency distribution is
(a) Ogive
(b) Histogram
(c) Frequency Polygon
(d) none
Q.6. Vertical bar chart may appear somewhat alike
(a) Histogram
(b) Frequency Polygon
(c) both
(d) none
Q.7. In Histogram, the classes are taken
(a) overlapping
(b) non-overlapping
(c) both
(d) none
Q.8.Consecutive rectangles in a Histogram have no space in between
(a) true
(b) false
(c) both
(d) none
Q.9.The breadth of the rectangle is equal to the length of the class-interval in
(a) Ogive
(b) Histogram
(c) both
(d) none
Q.10. Histogram emphasizes the widths of rectangles between the class boundaries.
(a) false
(b) true
(c) both
(d) none
Q.11. When all classes have equal width, the heights of the rectangles in Histogram will be
numerically equal to the
(a) class frequencies
(b) class boundaries
(c) both
(d) none
Q.12. Frequency density is used in the construction of
(a) Histogram
(b) Frequency Polygon
(c) Ogive
(d) none
Q.13. Unequal widths of classes in the frequency distribution do not cause any difficulty in the
construction of
(a) Ogive
(b) Frequency Polygon
(c) Histogram
(d) none
Q.14. In Histogram if the classes are of unequal width then the heights of the rectangles must be
proportional to the frequency densities.
(a) true
(b) false
(c) both
(d) none
Q.15. In representing simple frequency distributions of a discrete variable
(a) Ogive
(b) Histogram
(c) Frequency Polygon
(d) both b and c is useful.
Q.16. When all classes have a common width
(a) Pie Chart
(b) Frequency Polygon
(c) both
(d) none is used.
Q.17. When the width of all classes is same, frequency polygon has not the same area as the
Histogram.
(a) True
(b) false
(c) both
(d) none
Q.18. For obtaining frequency polygon we join the successive points whose abscissa represent the
corresponding class frequency_____
(a) true
(b) false
(c) both
(d) none
Q.19. The graphical representation of a cumulative frequency distribution is called
(a) Histogram
(b) Ogive
(c) both
(d) none.
Q.20. Diagrammatic representation of the cumulative frequency distribution is
(a) Frequency Polygon
(b) Ogive
(c) Histogram
(d) none
Q.21. Ogive is a
(a) line diagram
(b) Bar diagram
(c) both
(d) none
Q.22. An Ogive can be prepared in _____________ different ways.
(a) 2
(b) 3
(c) 4
(d) none
Q.23. The curve obtained by joining the points, whose x- coordinates are the upper limits of the
class-intervals and y coordinates are corresponding cumulative frequencies is called
(a) Ogive
(b) Histogram
(c) Frequency Polygon
(d) Frequency Curve
Q.24. Median of a distribution can be obtained from
(a) Frequency polygon
(b) Histogram
(c) Less than type ogives
(d) None of these.
Q.25. An approximate idea of the shape of frequency curve is given by
(a) Ogive
(b) Frequency Polygon
(c) both
(d) none
Q.26. Frequency curve is a limiting form of
(a) Frequency polygon
(b) Histogram
(c) (a) or (b)
(d) (a) and (b).
Q.27. Most of the commonly used frequency curves are
(a) Mixed
(b) Inverted J-shaped
(c) U-shaped
(d) Bell-shaped.
Q.28. The distribution of profits of a company follows
(a) J-shaped frequency curve
(b) U-shaped frequency curve
(c) Bell-shaped frequency curve
(d) Any of these.
ANSWERS
A
C
A
B
B
A
A
D
B
B
A
A
C
A
C
B
B
A
B
B
A
A
A
C
B
D
D
C
LAST YEAR EXAMS QUESTIONS
Q.1. Histogram is used for the presentation of the following type of series
(a) Time series
(b) Continuous frequency distribution
(c) Discrete frequency distribution
(d) Individual observation
Q.2. The most common form of diagrammatic representation of a grouped frequency distribution is
(a) Histogram
(b) Ogive
(c) Both
(d) None
Q.3. For constructing a histogram the class intervals of a frequency distribution must be of
the following type:
(a) Equal
(b) Unequal
(c) equal or unequal
(d) None of these
Q.4. An area diagram is
(a) Histogram
(b) Ogive
(c) Frequency polygon
(d) None of these
Q.5. Histogram can be shown as
(a) Ellipse
(b) Rectangle
(c) Hyperbola
(d) Circle
Q.6. Frequency density is used in the construction of
(a) Histogram
(b) Ogive
(c) Frequency polygon
(d) None
Q.7. With the help of histogram one can find
(a) Mean
(b) median
(c) mode
(d) first quartile
Q.8. Mode can be obtained from
(a) Frequency polygon
(b) histogram
(c) Ogive
(d) all of the above
Q.9.To draw histogram the frequency distribution should be
(a) inclusive type
(b) Exclusive type
(c) Inclusive and exclusive type
(d) none of these
Q.10. When the width of all classes is same frequency polygon has not the same area as the
histogram
(a) false
(b) true
(c) both
(d) None
Q.11. The graphical representation of a cumulative frequency distribution is called
(a) Histogram
(b) Ogive
(c) Both
(d) None
Q.12. If we plot less than and more than type frequency distribution then the graph plotted is
(a) Histogram
(b) frequency curve
(c) ogive
(d) None of these
Q.13. Curve obtained by joining the points whose x coordinates are the upper limits of the class
intervals and y coordinates are the corresponding cumulative are the corresponding cumulative
frequencies is called
(a) Frequency polygon
(b) frequency curve
(c) Histogram
(d) Ogive
Q.14. The graphical representation by which median is calculated is called
(a) ogive curve
(b) Frequency curve
(c) Line diagram
(d) Histogram
Q.15. Median of a distribution can be obtained from:
(a) Histogram
(b) Frequency polygon
(c) Less than type ogive
(d) None of these
Q.16. Using ogive curve we can determine
(a) Median
(b) quartile
(c) Both (a) and (b)
(d) None
Q.17. The intersection point of less than ogive and more than ogive gives
(a) Mean
(b) Mode
(c) median
(d) None of these
Q.18. Less than and more than type gives meet at a point known as:
(a) Mean
(b) median
(c) Mode
(d) None
Q.19. When the two curves of ogive intersect, the point of intersection provides
(a) First quartile
(b) Second quartile
(c) Third Quartile
(d) Mode
Q.20.The point of intersection of the “less than and “more than “ ogives correspond to
(a) mean
(b) Mode
(c) Median
(d) 10th percentile
Q.21. Quartiles can be determine graphically using
(a) Histogram
(b) Frequency polygon
(c) Ogive curve
(d) Pie chart
Q.22. From which graphical representation, we can calculate partition values?
(a) Lorenz curve
(b) Ogive curve
(c) Histogram
(d) None of these
Q.23. If we draw a perpendicular on x – axis from the point of intersection of both less than and
more than frequency curves we will get the value of ____
(a) Mode
(b) median
(c) arithmetic mean
(d) third quartile
Q.24. The less than ogive is a
(a) U – shaped curve
(b) J – shaped curve
(c) S – shaped curve
(d) Bell shaped curve
Q.25.The distribution of profit of a company follows:
(a) J – shaped frequency curve
(b) U – shaped frequency curve
(c) Bell – shaped frequency curve
(d) Any of these
ANSWERS
B
A
C
A
B
A
C
B
B
A
B
C
D
A
C
C
C
B
B
C
C
B
B
B
C
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