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Introduction to statistics - class-XII

Description: introduction to statistics
Number of Questions: 55
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Tags: introduction to statistical method and econometrics partition values maths frequency distribution tables and graphs economics statistics and probability statistics
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A branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data is called ______.

  1. mensuration

  2. statistics

  3. set theory

  4. survey


Correct Option: B
Explanation:

A branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data is called statistics.

_______ are sets of mathematical equations that are used to analyze what is happening in the world around us.

  1. Mensuration

  2. Survey

  3. Set theory

  4. Statistics


Correct Option: D
Explanation:

Statistics are sets of mathematical equations that are used to analyze what is happening in the world around us.

______ helps in providing a better understanding and exact description of a phenomenon of nature.

  1. Mensuration

  2. Survey

  3. Statistics

  4. Construction


Correct Option: C
Explanation:

Statistics helps in providing a better understanding and exact description of a phenomenon of nature.

______ helps in proper and efficient planning of a statistical inquiry in any field of study.

  1. Mensuration

  2. Survey

  3. Statistics

  4. Construction


Correct Option: C
Explanation:

Statistics helps in proper and efficient planning of a statistical inquiry in any field of study.

Statistics is the branch of mathematics that deals with the collection, organization, analysis, and interpretation of numerical ____.

  1. variables

  2. constant

  3. functions

  4. data


Correct Option: D
Explanation:

Statistics is the branch of mathematics that deals with the collection, organization, analysis, and interpretation of numerical data.

________ helps in presenting complex data in a suitable tabular, diagrammatic and graphic form for an easy and clear comprehension of the data.

  1. Mensuration

  2. Statistics

  3. Set theory

  4. Survey


Correct Option: B
Explanation:

Statistics helps in presenting complex data in a suitable tabular, diagrammatic and graphic form for an easy and clear comprehension of the data.

A contractor employed 18 labourers at Rs 12 per day 10 labourers at Rs 13.50 per day 5 labourers at Rs 25 per day and 2 labourers at Rs 42 per day The average wage of a labourer per day is

  1. Rs 16

  2. Rs 20

  3. Rs 24

  4. Rs 28


Correct Option: A
Explanation:

Total wages paid by contractor to 18 laborers Rs 12 per day =$18\times 12=216 Rs

And total wages paid by contractor to 10 laborers Rs 13.50 per day =$10\times 13.5=135 Rs
And total wages paid by contractor to 5 laborers Rs 25 per day =$5\times 25=125 Rs
And total wages paid by contractor to 2 laborers Rs 42 per day =$2\times 42=84 Rs
Then total wages paid by contractor to all laborers=216+135+125+84=560 Rs
And total  laborers=18+10+5+2=35
Then average wages =$\frac{560}{35}=16 $ Rs  

Bankers use ______ approaches to estimate the number of people who will be making deposits compared to the number of people requesting loans.

  1. manipulative

  2. statistical

  3. arithmetic

  4. data analytic


Correct Option: B
Explanation:

Bankers use statistical approaches to estimate the number of people who will be making deposits compared to the number of people requesting loans.

Number of students in your class is an example of ______.

  1. statistics

  2. mean

  3. mode

  4. median


Correct Option: A
Explanation:

Statistics is the collection of methods used in planning an experiment and analyzing data in order to draw accurate conclusions.
So, the number of students in your class is an example of statistics.

Which one of the following is not correct ?

  1. Statistics is liable to be misused

  2. The data collected by the investigator to be used by himself are called primary data

  3. Statistical laws are exact

  4. Statistics do not take into account of individual cases


Correct Option: C
Explanation:

Answer:- C) Statistical laws are exact.

Reason:-
The statistical laws are based on probability. Using probability we can only estimate the answer, it will not be accurate.
So statistical laws are not exact.

_____ deals with collection, organization and interpretation of data.

  1. Probability

  2. Statistics

  3. Both

  4. None of these


Correct Option: B
Explanation:

Answer:- B) Statistics

Explanation:-
Statistics deals with data moreover with its collection, organising it in a proper form and using it to analyze given situation i.e. interpretation.

A candidate who gets $20$% marks in an examination fails by $30$ marks but another candidate who gets $32$% gets $42$ marks more than the pass mark. Then, the percentage of pass mark is

  1. $52$

  2. $50$

  3. $33$

  4. $25$


Correct Option: D
Explanation:

Let the total marks be $x$.
According to the question,
$\dfrac {20}{100}\times x + 30 = \dfrac {32}{100} \times x - 42$
$42 + 30 = \dfrac {32}{100}x - \dfrac {20}{100}x$
$72\times 100 = 12x \Rightarrow x = 600$
Passing marks $= \dfrac {20}{100}x + 30 = \dfrac {20}{100}\times 600 + 30 = 150$
Required percentage $= \dfrac {150}{600}\times 100 = 25$%.

The lottery method is_________.

  1. very expensive

  2. very easy

  3. time saving

  4. time consuming and cumbersome


Correct Option: D
Explanation:

Lottery method can be time consuming if a large population or sample is involved in this and also it becomes a very tedious and ambiguous task.

Which of the following operations is conducted after a gap of every ten years?

  1. Economic survey

  2. Estimates of Foreign Direct Investment (FDI)

  3. Compilation of Human Development Report

  4. General Census


Correct Option: D
Explanation:

General census is official counting of a region's or nation's people and compilation of economics , social and other data usually for formulation of development policies and plans etc.

General census is an operation which is conducted after a gap of every ten years .

More practical and inexpensive method of sampling is__________.

  1. lottery method.

  2. use of table of random numbers.

  3. both (A) and (B).

  4. none of the above


Correct Option: B
Explanation:

Use of table of random numbers is less time consuming and less expensive as compared to lottery as lottery deals with a large set of population or samples and also it is a time consuming method.

In a random number table, each digit appears with___________.

  1. the same frequency

  2. independent of each other

  3. dependent of each other

  4. both (A) and (B)


Correct Option: D
Explanation:

In a random number table, every digit has got an equal probability of being appearing and are independent of each other as selection of one number is not influenced by any other number.

In which of the following cases is direct personal observation method adopted?

  1. Where greater accuracy is needed .

  2. When the field is an complex one

  3. When intensive study is needed

  4. All of the above


Correct Option: D
Explanation:

Direct personal observation is the method adopted so that an intensive study of the population can be done. Direct observation helps in getting accurate results as their behaviour can be easily ascertained.

In a predominantly illiterate area consisting of 10,000 population, data has to be collected from 10% of them. The appropriate technique for data collection would be ________.

  1. questionnaire

  2. schedule

  3. interview

  4. all of the above


Correct Option: A

The techniques of census investigation is advocated by its users because of _________________.

  1. intensive study i.e. It enables to study more than one aspect of each item of population

  2. reliability of data

  3. suitable choice in the situations when different items of population are not homogeneous

  4. All of above


Correct Option: D
Explanation:
Census investigation refers to the examining the whole population. It involves complete count. The technique of census investigation is advocated by its users because of the following reasons-
a) intensive study i.e. It enables to study more than one aspect of each item of population
b) reliability of data
c) suitable choice in the situations when different items of population are not homogeneous

The amount of non-responses is maximum in ___________________.

  1. mailed questionnaire method

  2. observation method

  3. interview method

  4. All of above


Correct Option: A
Explanation:

Under mailed questionnaire method, a well designed questionnaire is mailed to the informants with a request to fill it up and return the same within the specific time schedule. By this method, a wide range of people can be connected. The amount of non-responses is maximum in maid questionnaire method as most people are reluctant to answer the questions which are mailed.

In year $2011$, India has almost ____________ of world population.

  1. $1.22\%$

  2. $1.154\%$

  3. $17.50\%$

  4. $1.95\%$


Correct Option: C

By the $18^{th}$ century, the term ______ designated the systematic collection of demographic and economic data by states.

  1. statistics

  2. probability

  3. mensuration

  4. trigonometry


Correct Option: A
Explanation:

By the $18^{th}$ century, the term statistics designated the systematic collection of demographic and economic data by states.

At the beginning of the $20^{th}$ century, who developed the methods for decision making based on small set of data?

  1. Gottfried Achenwall

  2. William S Gosset

  3. W. Hooper

  4. Shakespeare


Correct Option: B
Explanation:

At the beginning of the $20^{th}$ century, William S Gosset has developed the methods for decision making based on small set of data.he has developed t-distribution theory.

The word statistics have been derived from Latin word ______.

  1. sanus

  2. status

  3. stella

  4. spes


Correct Option: B
Explanation:

The word statistics have been derived from Latin word "status".

In which year history of statistics can be said to start around?

  1. $1789$

  2. $1756$

  3. $1749$

  4. $1752$


Correct Option: C
Explanation:

The history of statistics can be said to start around in the year $1749$.

In the year $1602$, who used the word "statist" in his drama Hamlet?

  1. Charles Walker

  2. Jane West

  3. John Wallis

  4. William Shakespeare


Correct Option: D
Explanation:

William Shakespeare used the word statist in his drama Hamlet $1602$.

Since the population size is always larger than the sample size, then the sample statistic -

  1. Can never be larger than the population parameter

  2. Can never be equal to the population parameter

  3. Can never be zero

  4. Can never be smaller than the population parameter

  5. None of the above answers is correct.


Correct Option: E
Explanation:

Sample statistic will depend upon the sample chosen. 
It can be less than, greater than, equal to population parameter. 
It can assume the value of zero.
Ans-Option $E$.

Let $a$ and $b$, be positive real numbers. If $a,{A _1},{A _2},b$ are in $A.P$ and $a,{G _1},{G _2},b$ are in $G.P$ and $a,{H _1},{H _2},b$ are in $H.P$ ,then 
 $\frac{{{G _1}{G _2}}}{{{H _1}{H _2}}} = \frac{{{A _1} + {A _2}}}{{{H _1} + {H _2}}} = \frac{{\left( {2a + b} \right)\left( {a + 2b} \right)}}{{9ab}}$

  1. True

  2. False


Correct Option: A

The difference of maximum and minimum values in a data is called 

  1. class interval

  2. range

  3. frequency

  4. mean


Correct Option: B
Explanation:

Suppose that we had a data $A=\left{a _1,a _2.........a _n\right}$then

$Max.A=a _k, 1\leq k\leq n$
$minA=a _j, 1\leq j\leq n$
then for every $a _i\in A$
$a _j\leq a _i \leq a _k$
So,
$a _k-a _j$ is called range of A

Find the correct ascending order
$7, 5, 15, 12, 10, 11, 16$

  1. $5, 7, 10, 11, 12, 15, 16$

  2. $5, 7, 10, 11, 12, 16, 15$

  3. $5, 7, 11, 10, 12, 15, 16$

  4. None of these


Correct Option: A
Explanation:
Given order is $7,5,15,12,10,11,16$.
Ascending is low to high. 
Now rearranging the series, we get
$5,7,10,11,12,15,16$

A numerical value used as a summary measure for a sample, such as sample mean, is known as a:

  1. population parameter

  2. sample parameter

  3. sample statistic

  4. population mean


Correct Option: C
Explanation:

If it pertains to sample it is called a statistic, if it pertains to the population it is called a parameter.
Ans-Option $C$.

Find the correct descending order
$9.1, 3.7, 5.6, 8.3, 11.5, 10.6$

  1. $8.3,11.5, 10.6, 9.1, 5.6, 3.7$

  2. $11.5, 10.6, 9.1, 8.3, 5.6, 3.7$

  3. $11.5, 10.6, 9.1, 8.3, 3.7, 5.6$

  4. None of these


Correct Option: B
Explanation:

Given series is $9.1, 3.7, 5.6, 8.3, 11.5, 10.6$

Descending means high to low.
Therefore, descending order of the given series is $11.5, 10.6, 9.1, 8.3, 5.6, 3.7$.

Find the correct ascending order of $6.3, 5.9, 9.8, 12.3, 5.6, 4.7$.
  1. $4.7, 5.6,6.3,5.9. 9.8, 12.3$

  2. $4.7, 5.6, 5.9, 6.3, 12.3, 9.8$

  3. $4.7, 5.6, 5.9, 6.3, 9.8, 12.3$

  4. None of these


Correct Option: C
Explanation:
Given order is $6.3, 5.9, 9.8, 12.3, 5.6, 4.7$.
Ascending means low to high. 
Therefore, rearranging the given series again, we get $4.7, 5.6, 5.9, 6.3, 9.8, 12.3$

Find the correct descending order
$2, 0, 3, 4, 1, 2, 3, 5$

  1. $5, 4, 3, 2,3, 2, 1, 0$

  2. $5, 4, 3, 3, 2, 2, 1, 0$

  3. $4,5, 3, 3, 2, 2, 1, 0$

  4. $5, 4, 3, 3, 2, 2, 0,1$


Correct Option: B
Explanation:
Given, series is $2,0,3,4,1,2,3,5$
Descending means high to low.
Therefore, the descending order is $5,4,3,3,2,2,1,0$.

Which one of the following is not correct?

  1. Statistics is liable to be misused

  2. The data collected by the investigator to be used by himself are called primary data

  3. Statistical laws are exact

  4. Statistics do not take into account of individual cases


Correct Option: C
Explanation:

(A) Statistics is liable to be misused is wrong 

(B) the data collected by the investigator to be used simself are called primary data wrong
(C) Statistical laws are extract is correct
(D) statistics do not take into account of individual cases is wrong 
Then is the correct answer.

Which of the following represents statistical data?

  1. The names of owners of shops located in a shopping complex

  2. A list giving the names of all states of India

  3. A list of all European countries and their respective capital cities

  4. The volume of rainfall in a certain geographical area recorded every month for 24 consecutive months


Correct Option: D

A double graph is useful for _____ of data

  1. observation

  2. comparison

  3. seeking

  4. none of these


Correct Option: B
Explanation:

double graph is useful for comparison

Who introduced the first book of statistics in its title "Contribution to Vital Statistics"?

  1. Gottfried Achenwall

  2. Francis G.P. Neison

  3. Sir John Sinclair

  4. Johnson


Correct Option: B
Explanation:

Francis GP Neison introduced the first book of statistics in its title 'Contribution to Vital Statistics'.

______ was used by the British mainly for administrative and governmental bodies.

  1. Mensuration

  2. Calculation

  3. Statistics

  4. Geometry


Correct Option: C
Explanation:

Statistics was used by the British mainly for administrative and governmental bodies.

Which question can be answered by writing a numeral?

  1. What is your age?

  2. What is your father's name?

  3. What is your education?

  4. What is your ambition?


Correct Option: A
Explanation:

Numeral means numeric characters have to be involved. Numeric characters are numbers ranging from 0-1 and combinations between them.

Age has to contain a number,hence it is a numeral.
Name, education and ambition contain letters that is A to z and not numerals.
Hence only age can be answered by writing a numeral.

In order to draw meaningful inferences from any data, we need to _____ the data systematically

  1. raw

  2. organise

  3. unorganise

  4. none of these


Correct Option: B
Explanation:

Organised data is needed to draw meaningful inferences.

In which year was the word statistik used by German Gottfried Achenwall?

  1. $1730$

  2. $1750$

  3. $1729$

  4. $1749$


Correct Option: D
Explanation:

The word statistik used by German Gottfried Achenwall in the years $1749$.

The _____ stastistik, first introduced by Gottfried achenwall (1749), originally designated the data analysis of the state.

  1. Babylonian

  2. Egyptian

  3. Greek

  4. German


Correct Option: D
Explanation:

The German stastistik, first introduced by Gottfried ache wall $(1749)$, originally designated the data analysis of state.

The word statistics and statistical are derived from the Latin word status, means _______ state.

  1. stable

  2. political

  3. public

  4. geographic


Correct Option: B
Explanation:

The word statistics and statistical are derived from the Latin word status, means political state.

In $17^{th}$ century, which economist who used early statistical methods to analyses demographic data?

  1. Francis Galton

  2. Anders Nicolai

  3. Karl Pearson

  4. Sir William Petty


Correct Option: D
Explanation:

Sir William Petty, a $17^{th}$-century economist used early statistical methods to analyse demographic data.

The _____ Empire was the first government to gather extensive data about population, area and wealth of territories that they controlled.

  1. Greece

  2. Persian

  3. Roman

  4. British


Correct Option: C
Explanation:

The Roman Empire was the first government to gather extensive data about population, area and wealth of territories that they controlled.

Who is the founder of mathematical statistics?

  1. Francis Galton

  2. Anders Nicolai

  3. Karl Pearson

  4. Walter Weldon


Correct Option: C
Explanation:

Karl Pearson is the founder of mathematical statistics.

Which of the following is not a data collection method?

  1. Census

  2. Population

  3. Business strategy

  4. Tomato


Correct Option: D
Explanation:

Tomato is a not a data collection method, since tomato is a vegetable.
So, census, population and business strategy are types of methods of collection of data.

Which of the following is a data collection method?

  1. How many hours do you spend watching TV each week?

  2. How many books does our class check out of the library each week?

  3. How many pieces of candy are in the bag?

  4. What is your favorite flavor of ice cream?


Correct Option: B
Explanation:

How many books does our class check out of the library each week? is a collection of data method. Because in the library they will use the statistics method of enter the books in order to check out.
But in option $A, C$ and $D$ are habitual question we will ask to your friends.

If the population figures are given for each State of India, then the data can be classified as

  1. Qualitative

  2. Quantitatives

  3. Chronological

  4. Geographical


Correct Option: B
Explanation:

There are four important bases of classification:

(1) Qualitative Base (2) Quantitative Base (3) Geographical Base (4) Chronological or Temporal Base

(1) Qualitative Base:

When the data are classified according to some quality or attributes such as sex, religion, literacy, intelligence etc…

(2) Quantitative Base:

When the data are classified by quantitative characteristics like heights, weights, ages, income etc…

(3) Geographical Base:

When the data are classified by geographical regions or location, like states, provinces, cities, countries etc…

(4) Chronological or Temporal Base:

When the data are classified or arranged by their time of occurrence, such as years, months, weeks, days etc…


If the population figures are given for each State of India, then the data can be classified as quantitative data.

The statistical data are of two types. These types are

  1. Technical data and presentation data

  2. Primary data and secondary data

  3. Primary data and personal data

  4. None of these


Correct Option: B
Explanation:

The data is of two types, primary and secondary data.

Which one of the following represents statistical data?

  1. The names of all owners of shops located in a shopping complex.

  2. A list giving the names of all states of India.

  3. A list of all European countries and their respective capital cities.

  4. The volume of a rainfall in certain geographical area, recorded every month for 24 consecutive months.


Correct Option: D
Explanation:
$\Rightarrow$  Statistics is a very broad subject, with applications in a vast number of different fields.
$\Rightarrow$  Statistics is the methodology which scientists and mathematicians have developed for interpreting and drawing conclusions from collected data. 
$\Rightarrow$  Everything that deals even remotely with the collection, processing, interpretation and presentation of data belongs to the domain of statistics, and so does the detailed planning of that precedes all these activities.
$\Rightarrow$  Statistics consists of a body of methods for collecting and analyzing data.
$\therefore$  Option $D$ represent statistical data, since its collecting and analyzing the data.

The price of an article was increased by $r$%. Later the new price was decreased by $r$%. If the latest price was Re. $1$, then the original price was:

  1. Re. $1$

  2. Rs. $\left( \cfrac { 1-{ r }^{ 2 } }{ 100 } \right) $

  3. Rs. $\cfrac { \sqrt { 1-{ r }^{ 2 } } }{ 100 } $

  4. Rs. $\left( \cfrac { 10000 }{ 10000-{ r }^{ 2 } } \right) $


Correct Option: D
Explanation:
Let the original price of product be 'P'
Price increased by r%
$\therefore$ Increased price$=P\left( 1+\cfrac { r }{ 100 }  \right) $
New price decreased by r%
$\therefore $ Latest price$=\left[ P\left( 1+\cfrac { r }{ 100 }  \right)  \right] \left( 1-\cfrac { r }{ 100 }  \right) $
$=P\left( 1+\cfrac { { r }^{ 2 } }{ { 100 }^{ 2 } }  \right) $
Given latest price=Re. $1$
$\therefore P\left( 1+\cfrac { { r }^{ 2 } }{ { 100 }^{ 2 } }  \right) =1$
$P=$Rs. $\left( \cfrac { 10000 }{ 10000-{ r }^{ 2 } }  \right) $

A set of annual numerical data, comparable over the years, is given for the last $12$ years.
Consider the following statements:
$1.$ The data is best represented by a broken line graph, each corner (turning point) representing the data of one year.
$2.$ Such a graph depicts the chronological change and also enables one to make a short-term forecast.
Which of the above statements is/are correct?

  1. $1$ only

  2. $2$ only

  3. Both $1$ and $2$

  4. Neither $1$ nor $2$


Correct Option: A
Explanation:

The first statement is true as we can easily track the ups and downs of datat form 1 year to the next.

Statement 2 is false as the graph would require some kind of mathematical model to predict the short-term forecast and would not be helpful on its own. 

In industry statistics is applied in the following areas...

  1. Plant layout

  2. Quality control

  3. No. of vendors

  4. Transfers of Managers


Correct Option: B
Explanation:

In industries, statistics is applied majorly in areas of Quality Control.

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