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

The annual precipitation data of a city is normally distributed with mean and standard deviation as 1000 mm and 200 mm, respectively. The probability that the annual precipitation will be more than 1200 mm is

  1. < 50%

  2. 50%

  3. 75%

  4. 100%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a normal distribution, the mean is 1000. 1200 is one standard deviation (200) above the mean. Since the distribution is symmetric, the area above the mean is 50%, and the area above one standard deviation is less than 50%.

Multiple choice

Which of the following assertions are CORRECT? P: Adding 7 to each entry in a list adds 7 to the mean of the list Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list R: Doubling each entry in a list doubles the mean of the list S: Doubling each entry in a list leaves the standard deviation of the list unchanged

  1. P, Q

  2. Q, R

  3. P, R

  4. R, S
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Adding a constant to each entry shifts the mean by that constant but does not change the standard deviation. Doubling each entry doubles the mean and doubles the standard deviation. Thus, P and R are correct.

Multiple choice

The statistics of runs scored in a series by four batsmen are provided in the following table. Who is the most consistent batsman of these four?

   
Batsman Average Standard deviation
K 31.2 5.21
L 46.0 6.35
M 54.4 6.22
N 17.9 5.90

  1. K

  2. L

  3. M

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

Consistency means minimum deviation so ‘K’ is the most consistent batsman. Average is used, when we want to select the best batsman in the manner of run scoring.

Multiple choice statistics time series moving average and variation simple moving average

If one regression coefficient is greater than one, then other will be:

  1. Less than one

  2. More than one

  3. Equal to one

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

Both the regression coefficients $(b_{xy},b_{yx})$ must have the same sign. i.e., if one of them is positive other should positive or if one of them is negative other should be negative.

If one regression coefficient is greater than one, then other coefficient should be less than one.

Multiple choice statistics time series moving average and variation simple moving average

The sum of the difference between the actual values of $Y$ and its values obtained from the fitted regression line is always:

  1. Zero

  2. Positive

  3. Negative

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

Let the actual values be $y_1,y_2,...,y_n$

Let the values obtained from the fitted regression analysis be $\hat y_1,\hat y_2,...,\hat y_n$

Since, the values are obtained from the fitted regression line.
Therefore, the actual and obtained values are almost equal.
Therefore, $y_1=\hat y_1$, $y_2=\hat y_2$ , ... , $y_n=\hat y_n$

sum of the difference between the actual and obtained values is $(y_1-\hat y_1)+(y_2-\hat y_2)+...+(y_n-\hat y_n)=0$

Multiple choice statistics time series moving average and variation simple moving average

The regression lines will be perpendicular to each other if the coefficient of correlation r is equal to.

  1. $1$ only
  2. $1$ or $-1$
  3. $-1$ only
  4. $0$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The two regression lines are perpendicular to each other.

When coefficient of correlation is perfectly positive or negative $r$ = The two regression lines coincide 
Therefore the answer will be $1$ or $-1$
Multiple choice statistics time series moving average and variation simple moving average

Find the equation of $y$ on $x$ on the basis of the following data:

$x$ $5$ $2$ $1$ $4$ $3$
$y$ $5$ $8$ $4$ $2$ $10$
  1. $y=-0.8x+7$
  2. $y=0.4x+7$
  3. $y=-0.4x+7$
  4. $y=-0.4x-7$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
 $x$  $y$  $xy$  $x^2$
 5  5  25  25
 2  8  16  4
 1  4  4  1
 4  2  8  16
 3  10  30  9
 $\sum x=15$  $\sum y=29$  $\sum xy=83$  $\sum x^2=55$

The linear equation be y=a+bx

$n$ is the number of observations
$n=5$
where $a=\dfrac{(\sum y)(\sum x^2)-(\sum x)(\sum xy)}{n(\sum x^2)-(\sum x)^2}$
$\implies a=\dfrac{(29)(55)-(15)(83)}{5(55)-(15)^2}=\dfrac{350}{50}=7$
and $b=\dfrac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2}$
$\implies b=\dfrac{(5)(83)-(15)(29)}{5(55)-(15)^2}=\dfrac{-20}{50}=-0.4$
Therefore, $y=-0.4x+7$
Multiple choice statistics time series moving average and variation simple moving average

Consider the following statements: (1) If the correlation coefficient ${ r } _{ xy }=0$, then the two lines of regression are parallel to each other (2) If the correlation coefficient ${ r } _{ xy }=+1$, then the two lines of regression are perpendicular to each other? Which of the above statements is/are correct?

  1. 1 only

  2. 2 only

  3. Both 1 and 2

  4. Neither 1 nor 2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
If $r = 0\implies$ lines do not have anything common and hence, lines of regression are perpendicular.
when $r = 1\implies$ then the lines superimpose one another and hence, lines of regression are parallel/co-incident. So, both statements are wrong.
Multiple choice statistics time series moving average and variation simple moving average

Find the equation of $x$ on $y$ on the basis of the following data:

$x$ $2$ $4$ $6$ $8$ $10$
$y$ $6$ $5$ $4$ $3$ $2$
  1. $x+ 2y=14$
  2. $x-2y=14$
  3. $2x+ y=14$
  4. $2x- 2y=14$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the equation be $ax+by+c=0$


At $x=2 , y=6$
$\Rightarrow 2a+6b+c=0$

At $x=4, y=5$
$\Rightarrow 4a+5b+c=0$

At $x=6, y=4$
$\Rightarrow 6a+4b+c=0$

Solving these, we get
$a=1$
$b=$4
$c=-14$

$\therefore$ Equation is $x+2y=14$