Mathematics · Quantitative Aptitude

Statistics and Dispersion

559 Questions

Statistics and dispersion involve the calculation of mean, standard deviation, variance, and coefficient of variation for data sets. These questions also cover probability distributions and cumulative frequency analysis. Such quantitative aptitude topics are heavily featured in banking and SSC examinations.

Standard deviationNormal distributionMean calculationCumulative frequencyCoefficient of variation

Statistics and Dispersion Questions

Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

Why do we need an index number?

  1. helpful in measuring changes in value of money

  2. helful for business community

  3. in measuring labour quality

  4. All the above
Reveal answer Fill a bubble to check yourself
A,B Correct answer
Explanation

We need an index number because it is helpful in measuring changes in value of money and it is also helpful for business community.

Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

Index numbers can be used for:

  1. Forecasting

  2. Fixed prices

  3. Different prices

  4. Constant prices
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Index number can be used for Forecasting.
This index number is a useful number that helps us quantify changes in our field. It is easier to see one value than a thousand different values for each item in our field.

Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

Price relatives computed by chain base method are called: 

  1. Price relatives

  2. Chain indices

  3. Link relatives

  4. None of them
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\Rightarrow$  Price relatives computed by chain base method are called $Link\,\,relatives.$

$\Rightarrow$  Under this method, the base year’s price does not remain fixed but moves step from year to year. In other words, the immediately preceding year’s price becomes the base year’s price for each of the succeeding years.
$\Rightarrow$  Under this method, the base year’s price does not remain fixed but moves step from year to year. In other words, the immediately preceding year’s price becomes the base year’s price for each of the succeeding years.

$\Rightarrow$  $Chain\, index$ = $\dfrac{Average\, link\, relative\, of\, current\, year \times Chain\, index\, of\, previous\, year}{100}$

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

The sum of three consecutive odd numbers is $38$ more than the average of these numbers. What is the first number

  1. $13$
  2. $17$
  3. $19$

  4. Data inadequate

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
let $'a'$ be the first odd number

As per Question

$ a+a+2+a+4 = 38 +\dfrac{a+a+2+a+4}{3}$

$ \Rightarrow 3a+6 = 38+a+2 $

$ \Rightarrow 2a = 34$

$ \Rightarrow a = 17 $
Multiple choice maths operations on rational numbers rational numbers on number line rational numbers and their decimal expansions rational numbers between two rational numbers

There are 50 numbers Each numbers is subtracted from 53 and the mean of the numbers so obtained is found to be -3.5 The mean of the given numbers is 

  1. $48.9$
  2. $49.5$
  3. $52.5$
  4. $56.5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$   Total observation is $50$

$\Rightarrow$  Let sum of $50$ number be $x$
$\therefore$    $\dfrac{x-(50\times 53)}{50}=-3.5$
$\therefore$    $x-2650=-3.5\times 50$
$\therefore$    $x-2650=-175$
$\therefore$    $x=-175+2650$
$\therefore$    $x=2475$
$\Rightarrow$   Original mean = $\dfrac{2475}{50}=49.5$

Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

The average of certain first consecutive even number is $101$. Find their sum?

  1. $25,000$
  2. $33,600$
  3. $10100$
  4. $24,960$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The average of the first n consecutive even numbers (2, 4, 6, ..., 2n) is given by (2 + 2n)/2 = n + 1. We are given that the average is 101, so n + 1 = 101, which means n = 100. The sum of the first n consecutive even numbers is n(n + 1) = 100 * 101 = 10100.

Multiple choice

Which average is the number that appears in a set the most?

  1. mean

  2. median

  3. mode

  4. range
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The mode is defined as the value that appears most frequently in a data set. Mean is the average, median is the middle value, and range is the difference between the highest and lowest values.

Multiple choice maths frequency distribution tables and graphs introduction to statistics introduction to statistical method and econometrics partition values

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)
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

The average of the middle two rational numbers when  $\displaystyle {\frac{4}{7},\, \frac{1}{3},\, \frac{2}{5},\, \frac{5}{9}}$ are arranged in ascending order is

  1. $\displaystyle \frac{86}{90}$
  2. $\displaystyle \frac{86}{45}$
  3. $\displaystyle \frac{43}{45}$
  4. $\displaystyle \frac{43}{90}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The numbers are

$\displaystyle \frac { 4 }{ 7 } ,\quad \frac { 1 }{ 3 } ,\quad \frac { 2 }{ 5 } \quad & \quad \frac { 5 }{ 9 } $.
To  arrange them in ascending order, we make their denominators equal
to the L.C.M. of the denominators.
The L.C.M. of 7, 3, 5 & 9=315.
So $\displaystyle \frac { 4 }{ 7 } =\frac { 4\times 45 }{ 7\times 45 } =\frac { 180 }{ 315 } ,\ \displaystyle \frac { 1 }{ 3 } =\frac { 1\times 105 }{ 3\times 105 } =\frac { 105 }{ 315 } ,\ \displaystyle \frac { 2 }{ 5 } =\frac { 2\times 63 }{ 5\times 63 } =\frac { 126 }{ 315 } \quad &amp; \quad \ \displaystyle \frac { 5 }{ 9 } =\frac { 5\times 35 }{ 9\times 35 } =\frac { 175 }{ 315 } .\ \therefore \quad \displaystyle \frac { 105 }{ 315 } <\frac { 126 }{ 315 } <\frac { 175 }{ 315 } <\frac { 180 }{ 315 } \i.e \displaystyle \frac { 1 }{ 3 } <\frac { 2 }{ 5 } <\frac { 5 }{ 9 } <\frac { 4 }{ 7 } $.
Then, the average of the middle numbers
=$\displaystyle \frac { 1 }{ 2 } \left( \frac { 1 }{ 3 } +\frac { 2 }{ 5 }  \right) =\frac { 43 }{ 90 } $.
Ans- Option D.

Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

The average of the middle two rational numbers if $\displaystyle {\frac{4}{7},\, \frac{1}{3},\, \frac{2}{5},\, \frac{5}{9}}$ are arranged in ascending order is:

  1. $\displaystyle \frac{86}{90}$
  2. $\displaystyle \frac{86}{45}$
  3. $\displaystyle \frac{43}{45}$
  4. $\displaystyle \frac{43}{90}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle {\frac{4}{7},\, \frac{1}{3},\, \frac{2}{5},\, \frac{5}{9}}$
The above numbers in ascending order are
$\displaystyle {\frac{1}{3}\, <\, \frac{2}{5}\, <\, \frac{5}{9}\, <\, \frac{4}{7}}$
Middle two numbers are $\displaystyle \frac{2}{5}$ and $\displaystyle \frac{5}{9}$
$\therefore$ Average = $\displaystyle {\frac{2/5\, +\, 5/9}{2}\, =\, \frac{43}{90}}$

Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

The average of the middle two rational numbers if $\displaystyle \frac{4}{7},\, \displaystyle \frac{1}{3},\, \displaystyle \frac{2}{5},\, \displaystyle \frac{5}{9}$ are arranged in ascending order is

  1. $\displaystyle \frac{86}{90}$
  2. $\displaystyle \frac{86}{45}$
  3. $\displaystyle \frac{43}{45}$
  4. $\displaystyle \frac{43}{90}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle \frac{4}{7},\, \displaystyle \frac{1}{3},\, \displaystyle \frac{2}{5},\, \displaystyle \frac{5}{9}$
The above numbers in ascending order are
$\displaystyle \frac{1}{3}\, <\, \displaystyle \frac{2}{5}\, <\, \displaystyle \frac{5}{9}\, <\, \displaystyle \frac{4}{7}$
Middle two numbers are $\displaystyle \frac{2}{5}$ & $\displaystyle \frac{5}{9}$.
$\therefore$ Average = $\displaystyle \frac{\displaystyle \frac{2}{5}\, +\, \displaystyle \frac{5}{9}}{2}\, =\, \displaystyle \frac{43}{90}$.

Multiple choice economics planning and collecting data different types of data primary and secondary data collecting data

Simple random sample gives __________.

  1. equal chance to all items in the population

  2. preferences to some items in the population

  3. equal chance to all items in national income

  4. both (B) and (C)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simple random sampling refers to the process when every individual present in the population has an equal chance of being selected without any personal judgement.

Multiple choice commercial applications functioning of commercial organisation definition and functions of production department production or works department ideologies/concepts/views of marketing management

What is probability of rejecting the null hypothesis when it is true called?

  1. Type II error

  2. Type I error

  3. Standard error

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A Type I error occurs when a true null hypothesis is incorrectly rejected (false positive).

Multiple choice business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

The median of a symmetrical distribution, whose lower and upper quartiles are 60 and 80 respectively, is

  1. 60

  2. 80

  3. 70

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given,  lower quartile $=60$ and upper quartile $=80$ 
$\therefore$ median $=\frac{\mbox{
lower quartile
}+\mbox{
upper quartile
}}{2}=\dfrac{60+80}{2}=70$