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 economics and quantitative methods linear correlation spearman's coefficient of correlation spearman's rank correlation method correlation coefficients

If the correlation coefficient between $x$ and $y$ is $0.6$, covariance is $27$ and variance of $y$ is $25$, then what is the variance of $x$?

  1. $9/5$
  2. $81/25$
  3. $9$
  4. $81$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$Correlation \:coefficient = \dfrac{cov (x,y)}{std\: deviation (x) \times std\: deviation (y)}$

Let std deviation of $x$ be $x$.

We have $correlation \:coefficient=0.6, cov(x,y)=27, std\:deviation(y)=\sqrt{25}=5$

Substituting respective values

$0.6=\dfrac{27}{5\times x}$

$\Rightarrow x=9$

So variance of $x$ is $9^2=81$

Multiple choice business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

The mean of discrete obervations $y _1, y _2$ , ................ , $y _n$ is given by

  1. $\displaystyle \frac{\sum _{i=1}^{n} y _i}{n}$
  2. $\displaystyle \frac{\sum _{i=1}^{n} y _i}{\sum _{i=1}^{n}i}$
  3. $\displaystyle \frac{\sum _{i=1}^{n} y _i f _i}{n}$
  4. $\displaystyle \frac{\sum _{i=1}^{n} y _i f _i}{\sum _{i=1}^{n}y _if _i}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mean of terms = $\dfrac{Sum}{number}$


Therefore, Mean = $\displaystyle \dfrac{\sum _{i=1}^{n} y _i}{n}$

Multiple choice maths measure of central tendency assumed mean method assumed mean method of finding mean mean and median

Sum of squares of deviation of $10$ observations measured from $5$ is $17$ and sum of squares of observations is $170$ then mean of observation is

  1. $40.3$
  2. $4.5$
  3. $4$
  4. $4.03$
  5. $4.3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$x _1,x _2,x _3,x _4...x _10\x _1^2+x _2^2+x _3^2+x _4^2+....x _10^2=17 (Given) \rightarrow (i)$

$(x _1-5)^2+(x _2-5)^2+(x _3-5)^2+....+(x _10-5)^2=17(Given)\rightarrow (i)$
$Mean (M)=\cfrac{x _1+x-2+x _3+....x _10}{10}\ \Rightarrow x _1+x _2+x _3+....+x _10=10M\rightarrow(iii)$
From equation $(ii)$ we get
$x _1^2+25-10x _1+x _2^2+25-10x _2+x _3^2+25-10x _3+...+x _10^2+25-10x _10=17\ \Rightarrow (x _1^2+x _2^2+....x _10^2)-10(x _1+x _2+x _3+....+x _10)+25\times10=17\ \Rightarrow 170-10(10M)+250=17\ \Rightarrow420-100M=17\ \Rightarrow100M=403\ \Rightarrow M=\cfrac{403}{100}=4.03$

Multiple choice maths measure of central tendency assumed mean method assumed mean method of finding mean mean and median

The sum of the deviations of a set of values $x 1, x _2$, ...... $x _n$ measured from $50$ is $-10$ and the sum of deviations of the values from $46$ is $70$. The mean is __________.

  1. $49$
  2. $49.5$
  3. $49.75$
  4. $50$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sum of deviations from $50$ is $-10$


$\Rightarrow \sum(xi - 50) = -10$
     $\sum x _i - 50\sum1 = -10$
     $\sum x _i - 50n = -10$

$\therefore y-50n=-10.....(1)$

Sum of deviations from $46$ is $70$

$\Rightarrow \sum(x _i - 46) = 70$
     $\sum x _i - 46\sum1 = 70$
     $\sum x _i - 46n = 70$

$\therefore y-46n=70.....(2)$


Solving $(1)$ and $(2)$, we get
$4n = 80$ i.e. $n=20$

Putting value of $n$ in $(1)$, we get
$y=990$

Mean $= \dfrac{\sum x _i}{n} = \dfrac{y}{n} = \dfrac{990}{20} = 49.5$

Multiple choice computer and ms office mathematical methods for economics economics

Find the co-efficient of mean deviation from Median from the following data.Median deviation =4.2,Median =21

  1. 0.3

  2. 0.20

  3. 0.25

  4. 0.22
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The coefficient of mean deviation from the median is calculated as (Mean Deviation) / (Median). Here, 4.2 / 21 = 0.20.

Multiple choice business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

Number of patients in a hospital are discrete variable


If true then enter $1$ and if false then enter $0$

  1. $1$
  2. $0$

  3. can't determine

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

A discrete variable is one that can only take specific, countable values. Since you cannot have a fraction of a patient, the number of patients is a discrete variable.

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

Data on percentage distribution of area of land in acres owned by households in two districts of a particular state as follows:

Land holding District-A District-B
$0.01-0.99$ $5.62$ $13.53$
$1.0-2.49$ $18.35$ $21.84$
$2.5-7.49$ $47.12$ $39.32$
$7.5-12.49$ $19.34$ $12.15$
$12.5-19.99$ $7.21$ $7.43$
$20.0-29.99$ $2.36$ $5.73$

What is the appropriate diagram to represent the above data?

  1. Pie diagram

  2. Histogram

  3. Bar chart

  4. NONE OF THE ABOVE
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Appropriate diagram to represent given data is histogram because histogram easily represents graph of 2 different district on the same graph & in easy to understand graph

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

In a histogram, the area of each rectangle is proportional to the class size of the corresponding class interval? If not, correct the statement.
If true then enter $1$ and if false then enter $0$

  1. $1$
  2. $0$

  3. can't determine

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

No, this is not a correct statement.
In a histogram, horizontal axis represents the class intervals whose width is fixed & the varying data is plotted along the y-axis. So in all  the rectangles of a histogram, width remains same & the length changes.
So correct statement is "In a histogram, the area of each rectangle is proportional to the frequency of its class."

Multiple choice maths graphical representation histograms for non-uniform class widths histograms with unequal class intervals revisiting histograms

The shoppers who come to a departmental store are marked as : man (M), woman (W), boy (B) or girl (G). The following list gives the shoppers who came during the first hour in the morning.
W W W G B W W M G G M M W W W
W G B M W B G G M W W M M W W
W M W B W G M W W W W G W M M
W W M W G W M G W M M B G  G W

The mode shoppers are: 

  1. Women

  2. Men

  3. Boy

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

From the question we are going to form frequency table :

$Shoppers$  $No.\,of\,shoppers$ 
$M$  $15$ 
$W$  $28$ 
$B$  $5$ 
$G$  $12$ 

From table we can see, $Women(W)$ has maximum number of shoppers.

$\therefore$  The mode shoppers are $=Women$

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

Index for base period is always taken as: 

  1. $100$
  2. $1$
  3. $200$
  4. $0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  Index for base period is always taken as : $100$.

$\Rightarrow$  A base year is the first of a series of years in an economic or financial index. It is typically set to an arbitrary level of 100. 
$\Rightarrow$  New, up-to-date base years are periodically introduced to keep data current in a particular index. 
$\Rightarrow$  Any year can serve as a base year, but analysts typically choose recent years.