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

Which one is the not measure of dispersion.

A

The Range

B

50th Percentile

C

Inter-Quartile Range

D

Variance

Question 2

Statistic is a numerical quantity, which is calculated from:

A

Population

B

Sample

C

Data

D

Observations

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 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 5

The algebraic sum of deviations from mean is:

A

Maximum

B

Zero

C

Minimum

D

Undefined

Question 6

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

Question 7

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 8

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 9

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 10

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 11

Data in the Population Census Report is:

A

Grouped data

B

Ungrouped data

C

Secondary data

D

Primary data

E

Arrayed data

Question 12

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 13

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 14

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 15

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

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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 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 2

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

A

Zero

B

Maximum

C

Least

D

None

Question 3

The standard deviation is always _________ than mean deviation

A

Greater

B

Less

C

Equal

D

None

Question 4

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

A

6

B

zero

C

3

D

2

Question 4 Explanation:

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

Question 5

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

A

5 Var(X)

B

4 Var(X)

C

4 Var(X)+3

D

5 Var(X) + 3

Question 6

Lowest value of variance can be

A

1

B

-1

C

3

D

-3

E

0

Question 6 Explanation:

Variance can not be negative

Question 7

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 8

The sum of squares of deviation is least if measure from

A

Mean

B

Mode

C

Median

D

Variance

Question 9

Variance remains unchanged by change of

A

Origin

B

Scale

C

Both

D

None of these

Question 10

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 11

Variance is always calculated from

A

Mode

B

Varaince

C

Geometric Mean

D

Median

E

Mean

Question 12

The measure of dispersion is changed by a change of

A

Origin

B

Scale

C

Algebraic Signs

D

None

Question 13

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 14

A measure of dispersion is always ________

A

zero

B

Positive

C

Negative

D

Infinity

Question 15

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

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

Question 16

The variance of a constant is

A

zero

B

constant

C

a

D

None

Question 17

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 18

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 19

If the standard deviation of the values 2, 4, 6, 8 is 2.33, 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 20

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 21

The measure of Dispersion can never be

A

Positive

B

Negative

C

0

D

1

Question 22

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

A

1

B

0

C

Mean

D

Mode

E

Median

Question 23

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 24

Standard deviation is calculated from the Harmonic Mean (HM)

A

Always

B

Sometimes

C

Never

D

None of these

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

A

$\sum(X-12)^2$

B

$\sum(X-15)^2$

C

$\sum(X-14)^2$

D

$\sum(X-10)^2$

Question 6

The sum of values divided by their number is called

A

Median

B

Mode

C

None of these

D

Mean

E

Harmonic Mean

Question 7

Sum of deviations will be zero if it is taken from

A

Mode

B

Mean

C

Median

D

Standard Deviation

Question 8

Arithmetic Mean is ________ affected by extreme values

A

Highly

B

Not

C

Less

D

None of these

Question 9

_______ is based on all observations of data

A

None of these

B

Mean

C

Median

D

Mode

Question 10

The mean of a constant "b" is

A

Zero

B

None

C

b

Question 11

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

A

21

B

0

C

28

D

24

Question 12

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

A

9

B

70

C

0.9

D

90

Question 13

The average of first n natural numbers is

A

$\frac{n}{2}$

B

None of these

C

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

Question 14

The calculation of mean and variance is based on

A

Large values only

B

Small values only

C

All values

D

Extreme values only

Question 15

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

A

X

B

2X

C

nX

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Test 6

This test contains statistical MCQs about measure of central tendencies such as Geometric Mean (GM), Harmonic Mean (HM), Median, Mode and Arithmetic Mean (AM). Some of the MCQs are from different examinations relation to school, colleges, universities and Job related exams on statistics.

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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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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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”.

Matrices are everywhere. If you have used a spreadsheet program such as MS-Excel, Lotus or written a table (such as in Ms-Word) or even have used mathematical or statistical software such a Mathematica, Matlab, Minitab, SAS, SPSS and Eviews etc., you have used a matrix. Matrices make the presentation of numbers clearer and make calculations […]

In early civilizations, the number of animals (sheep, goat, and camel etc.) or children people have were tracked by using different methods such as people match the number of animals with the number of stones. Similarly, they count the number of children with the number of notches tied on a string or marks on a […]

The Z-Score The Z-score also referred to as standardized raw scores is a useful statistic because not only permits to compute the probability (chances or likelihood) of raw score (occurring within normal distribution) but also it helps to compare two raw scores from different normal distributions. The Z-score is a dimensionless measure since it is […]

Multicollinearity in Linear Regression Models The objective of multiple regression analysis is to approximate the relationship of individual parameters of a dependency, but not of interdependency. It is assumed that the dependent variable and regressors ‘s are linearly related to each other (Graybill, 1980; Johnston, 1963 and Malinvaud, 1968). Therefore, inferences depicted from any regression […]

Levels of Measurement (Scale of Measure) Level of measurement (scale of measure) have been classified into four categories. It is important to understand these level of measurement, since these level of measurement play important part in determining the arithmetic and different possible statistical tests that are carried on the data. The scale of measure is […]

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 […]

R language provides an interlocking suite of facilities that make fitting statistical models very simple. The output from statistical models in R language is minimal and one needs to ask for the details by calling extractor functions. Defining Statistical Models; Formulae in R Language The template for a statistical model is a linear regression model […]

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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”.

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