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 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

If $n^{th}$ term of AP is $4n+1$, then AM of $11^{th}$ to $ 20^{ th}$ terms is 

  1. $61.5$
  2. $63$
  3. $63.5$
  4. $62$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given: $t _{n}=4n+1$

$A.M.=\cfrac{t _{11}+t _{20}}{2}$
           $=\cfrac{4\times 11+1+4\times 20+1}{2}$
           $=63$

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

If  $n^{th}$ term of AP is $t _n=4n+1$. Find mean of first $10$ terms.   

  1. $85$
  2. $95$
  3. $23$
  4. $7.5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given:
$t _{n}=4n+1$
$\therefore A.M.=\dfrac{\sum _{n=1}^{10}4n+1}{n}$
               $=\dfrac{2n(n+1)+n}{n}$
               $=2n+3$
               $=2\times 10+3$
               $=23$
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 } $
$\therefore S=50\times 38=1900;\quad \therefore x=\cfrac { 1900-45-55 }{ 48 } =37.5$

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

Mean deviation of first $7$ natural no. about their A.M. is?

  1. $2$
  2. $\sqrt{2}$
  3. $\dfrac{12}{7}$
  4. $0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The first 7 natural numbers are 1, 2, 3, 4, 5, 6, 7. Their arithmetic mean (A.M.) is (1+2+3+4+5+6+7)/7 = 28/7 = 4. The absolute deviations from the mean 4 are |1-4|, |2-4|, |3-4|, |4-4|, |5-4|, |6-4|, |7-4|, which are 3, 2, 1, 0, 1, 2, 3. The sum of these deviations is 3+2+1+0+1+2+3 = 12. The mean deviation is therefore 12/7.

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

Find the average of the following set of scores $253,124,255,534,836,375,101,443,760$

  1. $427$
  2. $413$
  3. $141$
  4. $409$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find the average, sum all the given scores and divide by the total count of numbers. The sum of 253, 124, 255, 534, 836, 375, 101, 443, and 760 is 3681, and dividing by 9 yields 409.

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

Four numbers are in proportion. The sum of the square of the four numbers is $50$ and the sum of the means is $5$. The ratio of first two terms is $1 : 3$. What is the average of the four numbers ?

  1. $2$
  2. $3$
  3. $5$
  4. $6$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the four numbers in proportion be a, b, c, d, meaning ad = bc. The sum of the means (b + c) is 5, and the sum of their squares is a^2 + b^2 + c^2 + d^2 = 50. Using the ratio of the first two terms a : b = 1 : 3, we can find the values of the terms, leading to numbers whose sum is 12 and average is 12 / 4 = 3.