This section includes MCQs from importance of statistics, Variables (Quantitative, Qualitative or categorical) , Sources of Data (Primary and secondary), Representation of data (Classification of data, Tabulation of data, Frequency distribution, Graphical representation of data, Bivariate Frequency Distribution), Measure of Locations (Mean, Median, Mode, Weighted Mean, Geometric Mean, Harmonic Mean, Percentiles Deciles, Quartiles), Measure of dispersion (Range, Quartile Deviation, Mean deviation, Variance, Standard Deviation) etc.
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Question 1

The mean of a distribution is 14 and the standard deviation is 5. What is the value of the coefficient of variation?

A

60.4%

B

48.3%

C

35.7%

D

27.8%

Question 1 Explanation:

CV=$\frac{SD}{Mean}\times 100$

Question 2

The mean of a distribution is 23, the median is 24, and the mode is 25.5. It is most likely that this distribution is:

A

Positively Skewed

B

Symmetrical

C

Asymptotic

D

Negatively Skewed

Question 2 Explanation:

For Negative Skewed Mean is likely to be less than mode and median

Question 3

Which of the following describe the middle part of a group of numbers?

A

Measure of Variability

B

Measure of Central Tendency

C

Measure of Association

D

Measure of Shape

Question 4

According to the empirical rule, approximately what percent of the data should lie within $\mu \pm 2 \sigma$?

A

75%

B

68%

C

99.7%

D

90%

E

95%

Question 5

The sum of the deviations about the mean is always:

A

Range

B

Zero

C

Total Standard Deviation

D

Positive

E

Negative

Question 6

The middle value of an ordered array of numbers is the

A

Mode

B

Mean

C

Median

D

MidPoint

Question 7

Which of the following is not a measure of central tendency?

A

Percentile

B

Quartile

C

Standard deviation

D

Mode

Question 7 Explanation:

Standard Deviation is measure of Dispersion or variability its not measure of central tendency.

Question 8

Which of the following divides a group of data into four subgroups?

A

Percentiles

B

Deciles

C

Median

D

Quartiles

E

Standard Deviation

Question 9

If the standard deviation of a population is 9, the population variance is:

A

9

B

3

C

21

D

81

Question 9 Explanation:

variance is Square of standard deviation

Question 10

If a distribution is abnormally tall and peaked, then is can be said that the distribution is:

A

leptokurtic

B

pyrokurtic

C

platykurtic

D

mesokurtic

Question 10 Explanation:

A leptokurtic curve is "long peaked" . It is (lepto is Greek for thin or small; kurtos is Greek for bulge; thus, a curve which is "thin bulge").

Question 11

Sum of dots when two dice are rolled is

A

a discrete variable

B

a continuous variable

C

a constant

D

a qualitative variable

Question 12

The weights of students in a college/school is a

A

Discrete Variable

B

Continuous Variable

C

Qualitative Variable

D

None of these

Question 13

The number of accidents in a city during 2010 is

A

Discrete variable

B

Continuous variable

C

Qualitative variable

D

Constant

Question 14

Which of these represent qualitative data

A

Height of a student

B

Liking or disliking of (500) persons of a product

C

Income of a government servant in a city

D

Yield from a wheat plot

Question 15

Life of a T.V picture tube is a

A

Discrete variable

B

Continuous variable

C

Qualitative variable

D

Constant

Question 16

The first hand and unorganized form of data is called

A

Secondary data

B

Organized data

C

Primary data

D

None of these

Question 17

The data which have already been collected by some one are called

A

Raw data

B

Array data

C

Secondary data

D

Fictitious data

Question 18

Census reports used as a source of data is

A

Primary source

B

secondary source

C

Organized data

D

none

Question 19

The grouped data is also called

A

Raw data

B

Primary data

C

Secondary data

D

Qualitative data

Question 20

Primary data and _____________ data are same

A

Grouped

B

Secondary data

C

Ungrouped

D

None of these

Question 21

Questionnaire survey method is used to collect

A

Secondary data

B

Qualitative variable

C

Primary data

D

None of these

Question 22

Data collected by NADRA to issue computerized identity cards (CICs) are

A

Unofficial data

B

Qualitative data

C

Secondary data

D

Primary data

E

None of these

Question 23

Population census is conducted through

A

Sample survey

B

Accounting

C

Investigation

D

Complete enumeration

Question 24

A parameter is a measure which is computed from

A

Population data

B

Sample data

C

Test statistics

D

None of these

Question 25

Given $X_1=12, X_2=19 ,X_3=10, X_4=7$, then $\sum_{i=1}^4$ equals?

A

36

B

48

C

41

D

29

E

None of these

Question 25 Explanation:

12+19+10+7=48

Question 26

A chance variation in an observational process is

A

Dispersion/ Variability

B

Measurement error

C

Random error

D

Instrument error

Question 27

A constant variable can take values

A

Zero

B

Fixed

C

Not fixed

D

nothing

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Test 2

MCQs from Basic Statistics

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Question 1

When data are collected in a statistical study for only a portion or subset of all elements of interest we are using:

A

A sample

B

A Parameter

C

A Population

D

Both b and c

Question 2

Which branch of statistics deals with the techniques that are used to organize, summarize, and present the data:

A

Advanced Statistics

B

Probability Statistics

C

Inferential Statistics

D

Descriptive Statistics

E

Bayesian Statistics

Question 3

In statistics, conducting a survey means

A

Collecting information from elements

B

Making mathematical calculations

C

Drawing graphs and pictures

D

None of the above

Question 4

In inferential statistics, we study

A

the methods to make decisions about population based on sample results

B

how to make decisions about mean, median, or mode

C

how a sample is obtained from a population

D

None of the above

Question 5

You asked five of your classmates about their height. On the basis of this information, you stated that the average height of all students in your university or college is 67 inches. This is an example of:

A

Descriptive statistics

B

Inferential Statistics

C

Parameter

D

Population

Question 6

Statistic is a numerical quantity, which is calculated from:

A

Population

B

Sample

C

Data

D

Observations

Question 7

The algebraic sum of deviations from mean is:

A

Maximum

B

Zero

C

Minimum

D

Undefined

Question 8

The height of a student is 60 inches. This is an example of --------------

A

Qualitative data

B

Categorical data

C

Continuous data

D

Discrete data

Question 9

In statistics, a sample means

A

A portion of the sample

B

A portion of the population

C

all the items under investigation

D

none of the above

Question 10

Data in the Population Census Report is:

A

Grouped data

B

Ungrouped data

C

Secondary data

D

Primary data

E

Arrayed data

Question 11

In statistics, a population consists of:

A

All People living in a country

B

All People living in the are under study

C

All subjects or objects whose characteristics are being studied

D

None of the above

Question 12

In descriptive statistics, we study

A

The description of decision making process

B

The methods for organizing, displaying, and describing data

C

How to describe the probability distribution

D

None of the above

Question 13

Which one is the not measure of dispersion.

A

The Range

B

50th Percentile

C

Inter-Quartile Range

D

Variance

Question 14

Which of the following is not based on all the observations?

A

Arithmetic Mean

B

Geometric Mean

C

Harmonic Mean

D

Weighted Mean

E

Mode

Question 15

Which one of the following measurement does not divide a set of observations into equal parts?

A

Quartiles

B

Standard Deviations

C

Percentiles

D

Deciles

E

Median

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Test 3

MCQs about Measure of Dispersion I

This test contains MCQS about Measure of Dispersion/ Variation such as Standard Deviation, Variance, Mean Deviation, Coefficient of Variation, Moments, Symmetry and Skewness, Kurtosis, Quartiles Deviations, Range etc.

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Question 1

The variance of a constant is

A

zero

B

constant

C

a

D

None

Question 2

The mean deviation of the values, 18, 12, 15 is

A

6

B

zero

C

3

D

2

Question 2 Explanation:

$MD=\frac{\sum_{i=1}^n |x_i-\overline{x}|}{n}$

Question 3

Variance is always calculated from

A

Mode

B

Varaince

C

Geometric Mean

D

Median

E

Mean

Question 4

Lowest value of variance can be

A

1

B

-1

C

3

D

-3

E

0

Question 4 Explanation:

Variance can not be negative

Question 5

Variance remains unchanged by change of

A

Origin

B

Scale

C

Both

D

None of these

Question 6

Standard deviation is calculated from the Harmonic Mean (HM)

A

Always

B

Sometimes

C

Never

D

None of these

Question 7

$Var(2X+3)\,$ is

A

5 Var(X)

B

4 Var(X)

C

4 Var(X)+3

D

5 Var(X) + 3

Question 8

A measure of dispersion is always ________

A

zero

B

Positive

C

Negative

D

Infinity

Question 9

The percentage of values lies between $\overline{X}\pm 2 SD\,$ is

A

68.26%

B

95.45%

C

99.7%

D

65%

E

99%

Question 10

The variance of 5 numbers is 10. If each number is divided by 2, then the variance of new numbers is

A

20

B

5

C

2.5

D

5.5

E

0

Question 11

If the standard deviation of the values 2, 4, 6, 8 is 2.58, then the standard deviation of the values 4, 6, 8, 10 is

A

0

B

2.58

C

5

D

4.66

E

2.33

Question 12

If all values are same then the measure of dispersion will be

A

1

B

0

C

Mean

D

Mode

E

Median

Question 13

The standard deviation is always _________ than mean deviation

A

Greater

B

Less

C

Equal

D

None

Question 14

If X and Y are independent then SD (X − Y) is

A

$SD(X)-SD(Y)$

B

$SD(X)+SD(Y)$

C

$\sqrt{SD(X)+SD(Y)}$

D

$\sqrt{Var(X)+Var(Y)}$

Question 15

Mean Deviation, Variance and Standard Deviation of the values 4, 4, 4, 4, 4, 4 is

A

4

B

8

C

2

D

12

E

0

Question 16

The measure of dispersion is changed by a change of

A

Origin

B

Scale

C

Algebraic Signs

D

None

Question 17

The sum of squares of deviation is least if measure from

A

Mean

B

Mode

C

Median

D

Variance

Question 18

If Y=−8X − 5 and SD of X is 3, then SD of Y is

A

8

B

3

C

5

D

24

E

None

Question 19

The measure of Dispersion can never be

A

Positive

B

Negative

C

0

D

1

Question 20

For a symmetrical distribution approximately 68% of the cases are included between
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A

$\overline{X}-S\,$ and $\overline{X}+S$

B

$\overline{X}-2S\,$ and $\overline{X}+2S$

C

$\overline{X}-3S\,$ and $\overline{X}+3S$

D

None of these

Question 21

Which of these is a relative measure of dispersion
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A

Standard Deviation

B

Variance

C

Coefficient of Variation

D

Non of these

Question 22

The sum of squared deviations of a set of n values from their mean is

A

Zero

B

Maximum

C

Least

D

None

Question 23

Suppose for 40 observations, the variance is 50. If all the observations are increased by 20, the variance of these increased observation will be

A

50

B

70

C

50/20

D

50-20=30

E

50

Question 24

If a and b are two constants, then $Var(a + bX)\,$ is

A

$a\pm b Var(X)$

B

$Var(a) \pm Var(X)$

C

$\pm b Var(X)$

D

$b^2 Var(X)$

E

$(a \pm b) Var(X)$

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Test 4

MCQs about Measure of Dispersion II

Prepare yourself by taking http://itfeature.com 's online MCQs test about Measure of Dispersion/ Variation. It includes MCQs on Standard Deviation, Variance, Mean Deviation, Coefficient of Variation, Moments, Symmetry and Skewness, Kurtosis, Quartiles Deviations, Range etc.

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For a certain distribution if $\sum(x-2)=18, \sum(x-24)=0, \sum(x-28)=-24)$ then arithmetic mean is

A

24

B

28

C

0

D

21

Question 7

The average of first n natural numbers is

A

$\frac{n+1}{2}$

B

None of these

C

$\frac{n}{2}$

Question 8

The sum of squared deviation is least from

A

Median

B

Mode

C

Standard Deviation

D

Mean

Question 9

Which of the following is least if $\overline{X}=14$

A

$\sum(X-14)^2$

B

$\sum(X-15)^2$

C

$\sum(X-10)^2$

D

$\sum(X-12)^2$

Question 10

If C= A - B then $\overline{C}$ is

A

0

B

$\overline{A}+\overline{A}$

C

$\overline{X} \times \overline{Y}$

D

$\overline{A}-\overline{A}$

Question 11

The sum of values divided by their number is called

A

Mode

B

Harmonic Mean

C

None of these

D

Median

E

Mean

Question 12

The mean of 10 numbers is 9, then sum of these numbers will be

A

70

B

9

C

90

D

0.9

Question 13

The mean of a constant "b" is

A

Zero

B

None

C

b

Question 14

If "X" is a constant then $\sum_{i=1}^2 a =$ ________________

A

X

B

nX

C

2X

Question 15

Sum of deviations will be zero if it is taken from

A

Median

B

Standard Deviation

C

Mean

D

Mode

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Test 6

MCQS on Measure of Central Tendencies

This test covers MCQs on Measure of central tendencies such as Geometric Mean (GM), Harmonic Mean (HM), Median and Mode. This online test by http://itfeature.com will help you to pass your education or job related exam about subject statistics.

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Question 1

The Geometric Mean of -2, 4, 03, 6, 0 will be

A

Cannot be Computed

B

-3

C

0

D

3

E

None of these

Question 2

If any of the value in data set is zero then it is not possible (i.e. impossible) to compute

A

Median

B

Mean

C

Mode

D

Harmonic Mean

E

Geometric Mean

Question 3

If any of the value in data set is negative then it is impossible to compute

Student and Instructor of Statistics and business mathematics.
Currently Ph.D. Scholar (Statistics), Bahauddin Zakariya University Multan.
Like Applied Statistics and Mathematics and Statistical Computing.
Statistical and Mathematical software used are: SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel.
Like to use type-setting LaTeX for composing Articles, thesis etc.

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my name is Waqar Shah from pakistan BS in Statistics there i most test of Statistics are qualified and i want to register my degree in other county,
so if any one body know about it please tel me in details
like as taken test/exam to register my degree like as Engineer are register with Engineer Council.

I am so much happy to take part in your mcqs quizzes or tests, but one thing I wanna show you that please just complicate the questions more and more, for the sake of getting some competitive stuff and much more…

My name is yasir khalil and i am preparing my ppsc test for the post of statistical officer tell me the name of any approriate book which is available on internet……

my name is divakar and this site helped me alot in statistics please help me in one more thing also that is please give the solution of eachy and every question

sir G you have done excellent job but please allow the print and copy of the material from jehangir khan deputy controllero examinations university of Malakand.

Your provided reference of question in test 3 is not correct. Perhaps its question 3. Question 3 is correct as it says “The measure of dispersion is changed by a change of” and answer is “scale”.

In MCQs Basic Statistics 3 test, Q9 is “Lowest value of variance can be” and its answer is 0 which is correct.
and Q22 is “The percentage of values lies between $\overline{x} \pm 2\sigma$” and its answer is 95.45% which is also correct.

Please mention the actual questions or tell what is wrong with these questions.

We work with numbers in arithmetic, while in algebra we use numbers as well as Alphabets such as A, B, C, a, b, and c for any numerical values we choose. We can say that algebra is an extension of arithmetic. For example, the arithmetic sum of two numbers means that the sum of numbers […]

Absolute error of a measurement is the difference between the measured value of an object and its true value. When we take the measurement of an object, it is possible that the measured value is either a little more or a little lower than its true value, that is, an absolute error has occurred. For […]

In most of the everyday situations, we do not need to use highly sensitive measuring devices (instruments). the accuracy of our measurement depends on the purpose for which we use the information. Example: Suppose someone uses a compass as a guide in going from one end of the school to the other. It would not […]

Estimation is very useful especially when someone wishes to know whether he/ she has arrived at a logical solution to a problem under study. It is useful to learn about how to estimate the total sum of a bill to avoid immediate overpayments. For example, one can estimate the total amount of a shop (supermarket) […]

A bivariate relationship is defined by the joint distribution of the two associated random variables. Contingency Tables Let and are two categorical response variables. Let variable have levels and variable have levels. The possible combinations of classifications for both variables are . The response of a subject randomly chosen from some population has a probability […]

In R language, the packages can have namespaces, and currently, all of the base and recommended packages do except the dataset packages. Understanding the use of namespaces is vital if one’s plan to submit a package to CRAN because CRAN requires that the package plays nicely with other submitted packages on CRAN. Namespaces ensure that […]

In R Language, a vector is the simplest data structure. A vector in R is also an object that contains elements having the same data type. To create a vector (say ‘x’) of the same type (say double) of elements consisting of five elements one can use c() function. For example, Creating a vector in […]

Reading and Writing Data in R Reading Data in R For reading (importing) data into R following are some functions. read.table(), and read.csv(), for reading tabular data readLines() for reading lines of a text file source() for reading in R code files (inverse of dump) dget() for reading in R code files (inverse of dput) […]

In R language, list is an object that consists of an ordered collection of objects known as its components. A list in R Language is a structured data that can have any number of any modes (types) of other structured data. That is, one can put any kind of object (like vector, data frame, character […]

The R program’s structure is similar to the programs written in other computer languages such as C or its successors C++ and Java. However, important differences between these languages and R are (i) R has no header files, (ii) most of the declarations are implicit, (iii) there are no pointers in R, and (iv) text […]

The problem of multicollinearity plagues the numerical stability of regression estimates. It also causes some serious problem in validation and interpretation of the regression model. Consider the usual multiple linear regression model, , where is an vector of observation on dependent variable, is known design matrix of order , having full-column rank , is vector of […]

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sir G you have done excellent job but please allow the print and copy of the material from jehangir khan deputy controllero examinations university of Malakand.

where we find the correct answers.. the test is only showing tht wht is correct or wrong

Answers are in pdf file. You can also see correct answer if you click all (or few) options in a question.

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very helpfull, great job

q#8 of test 3 is wrong according to my knowldge …please explain.i think standerd deviation is not effected by change of origin

Your provided reference of question in test 3 is not correct. Perhaps its question 3. Question 3 is correct as it says “The measure of dispersion is changed by a change of” and answer is “scale”.

grt job …hv u uploded mor statistics mcqs

shr link plz

sir ? checkout query 14

Please share the Quiz number, name or path of the Quiz. Otherwise Query 14 cannot be checked.

very informative.

Bhai this is a site what I am looking for …….so much helpful for us …… lots of thanks for your efforts .

sir really i have impressed and very informative thanks sir for improving our knowledge

Very good website for online test practise

i learnt more from this than all my studies on status so far , thank u !!!!

sir in test three answers of question no 9 and 22 are wrong pls. correct them

In MCQs Basic Statistics 3 test, Q9 is “Lowest value of variance can be” and its answer is 0 which is correct.

and Q22 is “The percentage of values lies between $\overline{x} \pm 2\sigma$” and its answer is 95.45% which is also correct.

Please mention the actual questions or tell what is wrong with these questions.

Good Source of Learning

very good mcq sir

Q22 on this of Test 3 “MCQs about Measure of Dispersion I” is wrong . instead of 2.33 this should be 2.58

thank. correction is made.

This site is so helpful,thank you so much MR Muhammad,I can now final say i am ready for a statistics test

Very informative