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 maths average arithmetic mean of ap introduction to averages means

Suppose a population $A$ has $100$ observations $101,102...200$ and other population $B$ has $100$ observations $151,152...250$. 

Find the difference in their means

  1. $49$
  2. $50$
  3. $51$
  4. $52$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The observations of $A$ are $101,102,......,200$

The sum is $\dfrac{100}{2}[2(101)+(100-1)1]\50(202+99)\50(301)=15050$
Mean is $\dfrac{15050}{100}\150.5$
The observations of $B$ are $151,152,......,250$
The sum is $\dfrac{100}{2}[2(151)+(100-1)1]\50(302+99)\50(401)=20050$
Mean is $\dfrac{20050}{100}=200.50$
The difference is $200.5-150.5=50$

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

The mean of $3$ observations is $12$ and mean of $5$ observations is $4$ the combined mean is 

  1. 7

  2. 8

  3. 9

  4. 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The no .of  observations is $3+5=8$

The sum of observations is $3(12)+5(4)=36+20=56$
The mean is $\dfrac{56}{8}=7$

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

The arithmetic mean of first ten natural numbers is

  1. $5.5$
  2. $6$
  3. $7.5$
  4. $10$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The arithmetic mean of first ten natural numbers is the average of these natural numbers.


$\therefore$ arithmetic mean

   $=\dfrac{1+2+3+4+5+6+7+8+9+10}{10}$

   $=\dfrac{n(\dfrac{n+1}{2})}{10}\,\,\,\,\,\,\,\rightarrow Here \,\boxed{n=10}$

   $=\dfrac{10\times \dfrac{11}{2}}{10}$ 

   $=\dfrac{11}{2}=\boxed{5.5}\rightarrow $ option -A

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

The A.M. of 'n' observations is M. If the sum of $(n - 4)$ observation is 'a', what is the mean of remaining $4$ observations?

  1. $nM + a$
  2. $\dfrac {nM - a}{2}$
  3. $\dfrac {nM + a}{2}$
  4. $\dfrac {nM - a}{4}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given $\cfrac { { a } _{ 1 }+{ a } _{ 2 }+{ a } _{ 3 }+{ a } _{ 4 }+....+{ a } _{ n } }{ n } =M\quad \quad \quad (1)\\ \left( { a } _{ 1 }+{ a } _{ 2 }+{ a } _{ 3 }+{ a } _{ 4 }+....+{ a } _{ n-4 } \right) =a\quad \quad \quad (2)$

From $(1)$ and $(2)$
$a+{ a } _{ n-3 }+{ a } _{ n-2 }+{ a } _{ n-1 }+{ a } _{ n }=nM\\ { a } _{ n-3 }+{ a } _{ n-2 }+{ a } _{ n-1 }+{ a } _{ n }=(nM-a)\\ Mean=\cfrac { { a } _{ n-3 }+{ a } _{ n-2 }+{ a } _{ n-1 }+{ a } _{ n } }{ 4 } =\cfrac { nM-a }{ 4 } \\ Mean=\cfrac { (nM-a) }{ 4 } $
Multiple choice maths average arithmetic mean of ap introduction to averages means

The arithmetic mean (average) of the first $n$ positive integers is

  1. $\dfrac {n}{2}$
  2. $\dfrac {n^{2}}{2}$
  3. $n$
  4. $\dfrac {n - 1}{2}$
  5. $\dfrac {n + 1}{2}$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The sum of the first $n$ positive integers is $s = \dfrac {n(n + 1)}{2}$. Since $A.M. = \dfrac {s}{n}$, the correct choice is (e).