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 measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

The following data show the number of hours worked by 200 statistics students:

Number of Hours Frequency
0-9 40
10-19 50
20-29 70
30-39 40

The class width for this distribution is.........

  1. 9

  2. 10

  3. 11

  4. Varies from class to class
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Class width is the difference between the upper boundary of a class and the lower boundary. For 0-9, 10-19, the width is 10 - 0 = 10.

Multiple choice statistics vital statistics and official statistics guiding rules for tabulation vital statistics textual and tabular presentation of data

Let m be the mid-point be the upper class limit of a continuous frequency distribution The lower class limit of the class is

  1. $2m+L$
  2. $2m-L$
  3. $m-L$
  4. $m+2L$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Mid point=$\dfrac{upper  limit+ lower  limit}{2}$

$\Rightarrow m=\dfrac{L+lower  limit}{2}$
$\Rightarrow Lower   limit=2m-L$

Multiple choice statistics vital statistics and official statistics guiding rules for tabulation vital statistics textual and tabular presentation of data

The class marks in a frequency table are given to be $5,10,15,20,25,30,35,40,45,50$. The class limits of the first classes are 

  1. $3-7,7-17,13-17,17-23,23-27$
  2. $2.5-7.5,7.5-12.5,12.5-17.5,17.5-22.5,22.5-27.5$
  3. $1.5-8.5,8.5-11.5,11.5-18.5,18.5-21.5,21.5-28.5$
  4. $2-8,8-12,12-18,18-22,22-28$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$2.5 - 7.5, 7.5 - 12.5, 12.5 - 17.5, 17.5 - 22.5, 22.5 - 27.5$


Given,

$5,10,15,20,25,30,35,40,45,50$

the class limit is given by,

$\dfrac{5}{2}=2.5$

$\dfrac{5+10}{2}=7.5$

$\dfrac{10+15}{2}=12.5$

$\dfrac{15+20}{2}=17.5$

$\dfrac{20+25}{2}=22.5$

$\dfrac{25+30}{2}=27.5$

Multiple choice statistics vital statistics and official statistics guiding rules for tabulation vital statistics textual and tabular presentation of data

The class marks of a frequency distribution are given as follow 15,20,25,...
The class corresponding to the class mark 20 is 

  1. $12.5-17.5$
  2. $17.5-22.5$
  3. $18.5-21.5$
  4. $19.5-20.5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Width=5

Class marks=20
$\therefore  Lower\  limit=20-\dfrac{5}{2}$
$\Rightarrow \dfrac{40-5}{2}=\dfrac{35}{2}=17.5$
$Upper\  limit=20+\dfrac{5}{2}$
$\Rightarrow \dfrac{40+5}{2}=\dfrac{45}{2}=22.5$
Hence the class corresponding to the class mark 20 is $17.5-22.5.$

Multiple choice business economics and quantitative methods linear regression aspects of correlation scatter graphs and correlation correlation

Co-variance between two variables is _____________.

  1. the average of the product of deviations taken from their averages

  2. a is further divided by the product of their standard deviations

  3. a is further divided by the product of their arithmetic averages

  4. none of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Covariance is defined as the average of the products of the deviations of two variables from their respective means: Cov(X,Y) = E[(X - E[X])(Y - E[Y])].

Multiple choice business economics and quantitative methods linear regression aspects of correlation scatter graphs and correlation correlation

The angle between the two lines will be wider when the correlation between two variable is___________.

  1. less

  2. more

  3. equal

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

The larger the angle between the two regression lines, less the degree of correlation between the two variables and similarly, the small the angle between two lines, the larger would be the degree of correlation between them.

Multiple choice business economics and quantitative methods correlation analysis aspects of correlation scatter graphs and correlation linear regression

When r=0, the lines of regression will____________.

  1. intersect each other at $90^o$

  2. be positive slope

  3. be negative slope

  4. be convex to the origin
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When the correlation coefficient r is 0, there is no linear relationship between the variables. Consequently, the two regression lines are perpendicular to each other, intersecting at a 90-degree angle.

Multiple choice business economics and quantitative methods correlation analysis aspects of correlation scatter graphs and correlation linear regression

When r = +1, the lines of regression will_____________.

  1. be positive slope

  2. move upwards from left to right

  3. be negative slope

  4. both (A) and (B)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When coefficient of correlation is +1, it is referred to as perfect positive correlation and the two lines of regression coincide and it has a positive slope.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

Lowest value of variance can be:

  1. $1$
  2. $-1$
  3. $0$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
We know that $Var(x)=E(X^2)-(E(x))^2$

Variance is non-negative because the squares are positive or zero.

Therefore, $Var(X)\geq 0$

Hence, the lowest value of variance is $zero$
Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

What is the standard deviation of $7,9,11,13,15$?

  1. $2.4$
  2. $2.5$
  3. $2.7$
  4. $2.8$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given numbers are $ 7,9,11,13,15$
Mean of given numbers $=\dfrac { 7+9+11+13+15 }{ 5 } =11$
Standard deviation$=\dfrac { |7-11|+|9-11|+|11-11|+|13-11|+|15-11| }{ 5 } =2.4$
Option A is true

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

__________ is the positive square root of the mean of squared deviations from mean. 

  1. Mean Deviation

  2. Standard Deviation

  3. Quartile Deviation

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

Standard deviation is defined mathematically as the square root of the variance, which is the mean of the squared deviations from the arithmetic mean.