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 business maths random variables and probability distribution poisson distribution poisson distrubution probability distributions

If ${ \mu  } _{ 2 }=20,{ \mu  } _{ 2 }^{ 1 }=276$ for a discrete random variable $X$, then the mean of the random variable $X$ is

  1. $16$
  2. $5$
  3. $2$
  4. $1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\mu _2=E(X^2)-[E(X)]^2......(i)$

$\mu _2'=E(X)^2.....(ii)$
Given: $\mu _2=20, \mu _2'=276$
from equation (ii) $\implies E(x^2)=276$
and from equation (i), $\implies 20=276-[E(X)]^2$
$\implies [E(X)]^2=276-20=250\\implies E(X)=16$
is the mean of random variable.

Multiple choice maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

If average of $6$ consecutive numbers is $48$, what is the difference between the smallest and the largest numbers ?

  1. $5$
  2. $10$
  3. $9$

  4. data inadequate
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the $6$ numbers are $x, x+1, x+2, x+3, x+4, x+5$.

Since,
$average=48$
$\dfrac{x+x+1+x+2+x+3+x+4+x+5}{6}=48$
$6x+15=288$
$6x=273$
$x=45.5$
So,
The smallest number $=45.5$
The largest number $=x+5=45.5+5=50.5$
Difference $=50.5-45.5=5$

Multiple choice maths average arithmetic mean of ap introduction to averages means

The mean of ${1^{2,}}{2^2},{3^2},{4^2},{5^2},{6^2},{7^2}$ is:

  1. 10

  2. 20

  3. 30

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

The sum of squares of the first 7 natural numbers is 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 = 1 + 4 + 9 + 16 + 25 + 36 + 49 = 140. The mean is 140 / 7 = 20.

Multiple choice maths average arithmetic mean of ap introduction to averages means

If each observation is multiplied by $\displaystyle \frac{1}{3}$ then the mean of the new data will de

  1. $\displaystyle \frac{1}{3}$ times

  2. 3 times
  3. $\displaystyle \frac{1}{\sqrt{3}}$ times
  4. $\displaystyle \frac{2}{3}$ times
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let set of data is 9,10,11,17 and 13

Then mean =$\frac{9+10+11+17+13}{5}=\frac{60}{5}$
If Each observation is multiply by $\frac{9+10+11+17+13}{5}=\frac{60}{5}=12$
Then data are $\frac{9}{3},\frac{10}{3},\frac{11}{3},\frac{17}{3}and \frac{13}{3}$
Then sum of data=$\frac{9}{3}+\frac{10}{3}+\frac{11}{3}+\frac{17}{3}+ \frac{13}{3}=\frac{60}{3}=20$
Then new mean of data=$\frac{20}{5}=4$
Then new data mean =$\frac{4}{12}=\frac{1}{3}$ times of old data

Multiple choice maths average arithmetic mean of ap introduction to averages means

Find the arithmetic mean of the progression $2, 4, 6, 8, 10.$

  1. $10$
  2. $20$
  3. $30$
  4. $6$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the formula for Required arithmetic mean $=\dfrac{\text{sum of the terms}}{\text{number of terms}}$


After substituting the values we get$=\dfrac{2+4+6+8+10}{5}=\dfrac{30}{5}=6$

Multiple choice maths average arithmetic mean of ap introduction to averages means

Find the arithmetic mean of first $10$ natural numbers.

  1. $55$
  2. $550$
  3. $5.5$

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

Arithmetic mean of first 10 natural numbers is:

$=\dfrac{1+2+3+4+5+6+7+8+9+10}{10}$
$=\dfrac{(\dfrac{n.(n+1)}{2})}{10}$,  where $n=10$. 
$=\dfrac{(\dfrac{10.11}{2})}{10}$
$=5.5$                                             

Multiple choice maths average arithmetic mean of ap introduction to averages means

The  arithmatic mean of $4,6,8$ is

  1. $4$
  2. $6$
  3. $8$
  4. $4.5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  First adding numbers $4,\, 6$ and $8$ = $4+6+8=18$

$\Rightarrow$   We have number of terms 3
$\Rightarrow$   $Arithemetic\, mean=\dfrac{S}{N}=\dfrac{18}{3}=6$

Multiple choice maths average arithmetic mean of ap introduction to averages means

The arithmetic mean (average) of a set of $50$ numbers is $38$. If two numbers, namely, $45$ and $55$, are discarded, the mean of the remaining set of numbers is :

  1. $36.5$
  2. $37$
  3. $37.2$
  4. $37.5$
  5. $37.52$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$Arithmetic\quad sum=\cfrac { sum\quad of\quad numbers }{ number\quad of\quad numbers } $
$\therefore S=50\times 38=1900;\quad \therefore x=\cfrac { 1900-45-55 }{ 48 } =37.5$