Mathematics · Quantitative Aptitude

Statistics and Dispersion

515 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 botany plant water relation diffusion pressure deficit other pressure components osmosis in plants

In a fully turgid cell, the values of DPD, OP and TP will show the tendency

  1. DPD$=$10atm, OP$=$15atm, TP$=$5atm
  2. DPD$=$5atm, OP$=$12atm, TP$=$7atm
  3. DPD$=$2atm, OP$=$7atm, TP$=$5atm
  4. DPD$=$0atm, OP$=$15atm, TP$=$15atm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In a fully turgid cell there will be no net movement of water. Neither water will move inside nor move outside. This is because DPD will be zero. DPD can be zero, when the osmotic pressure, which causes movement of water inside the cell equals to turgor pressure, which opposes the entry of water inside the cell.

Multiple choice maths bar graphs histograms for non-uniform class widths histograms with unequal class intervals revisiting histograms

Sum of all components in normalized histogram is equal to

  1. $0$
  2. $2$
  3. $100$
  4. $1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\Rightarrow$  Sum of all components in normalized histogram is equal to $1$

$\Rightarrow$  The histogram of a digital image with intensity levels in the range $[0,L-1]$ is a discrete function, $h(r _k)=n _k$, where, $r _k$ is $k^{th}$ intensity value and $n _k$ is the number of pixels in the image with intensity, $r _k$.
$\Rightarrow$  It is a common practice to normalize a histogram by dividing each of its components by total number of pixels in the image, denoted by a matrix $M\times N$, where $M$ and $N$ are the row and column dimension of the image. Thus a normalized histogram is given by the following equation,

$P(r _k)=\dfrac{n _k}{M\times N}for\,k=0,1...L-1$

Multiple choice economics consumption and investment functions keynesian law of consumption and propensity to consume ex ante and ex post concept of consumption function, saving function and investment function

The Average Propensity to Consume is denoted as _____________.

  1. $APC=\dfrac{C}{I}$
  2. $APC=\dfrac{S}{Y}$
  3. $APC=\dfrac{I}{Y}$
  4. $APC=\dfrac{C}{Y}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
 APC refers to Average Propensity to Consume which defines the amount of consumption in every 1 rupee of income for all level of income. 
Average propensity to consume = C/Y 
where C is the consumption and Y is the income in the economy.
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

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 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 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 $=\frac{\mbox{
lower quartile
}+\mbox{
upper quartile
}}{2}=\dfrac{60+80}{2}=70$

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 middle value of an ordered series is called _______.

  1. $2nd$ quartile
  2. $5th$ decile
  3. $50th$ percentile

  4. All the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The median divides an ordered series into two equal halves. The 2nd quartile (Q2), 5th decile (D5), and 50th percentile (P50) all represent this same middle point.

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

Inter-Quartile Range is based upon ________.

  1. First 50% of the values

  2. middle 50% of the values

  3. Last 50 % of the values

  4. 25% of the values
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The interquartile range is the difference between the third quartile (Q3) and the first quartile (Q1), which encompasses the middle 50% of the data.