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 some mathematical tools used in economics step towards making a project basic statistics for economics economics

The class interval of the following continuous grouped data is
0-9    10-19     20-29     30-39     40-49
5           8           12           15           4

  1. 10

  2. 9

  3. 24.5

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

The class interval (or class width) is the difference between the upper and lower boundaries of a class. For 0-9, 10-19, etc., the width is 10 - 0 = 10.

Multiple choice some mathematical tools used in economics step towards making a project basic statistics for economics economics

The distribution.
Values (less than)               20  25   30   35  40  45  50
Frequency is of the type     5   12    15   20  15   10   5 

  1. exclusive class type

  2. discrete type

  3. inclusive class type

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

The data provided is in a 'less than' cumulative frequency format, which is characteristic of an exclusive class type distribution where the upper limit of one class is the lower limit of the next.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

The average of 9  consecutive numbers with difference of 9 is 79 , then with smallest number  among them ?

  1. 43

  2. 34

  3. 52

  4. 44
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For 9 numbers with difference 9, the average is the middle number (the 5th number). So 5th number = 79. The sequence is 79-4*9, 79-3*9, 79-2*9, 79-9, 79, 79+9, ... Smallest = 79 - 36 = 43.

Multiple choice

What is the average of 4, 8, 6?

  1. 18

  2. 6

  3. 9

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find the average, sum the numbers (4 + 8 + 6 = 18) and divide by the count (3). 18 / 3 = 6.

Multiple choice statistics data handling analysis bar charts frequency table and diagrams bar diagram

The following frequency distribution is classified as 
X : 0   1    2   3   4   5   6  
f:    2   5   8   10   9   6   3    

  1. continuous distribution

  2. discrete distribution

  3. cumulative frequency distribution

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

A discrete distribution represents data where variables take on specific, distinct values (like 0, 1, 2, etc.) rather than a continuous range. Since the variable X is listed as distinct integers, this is a discrete distribution.

Multiple choice statistics data handling analysis bar charts frequency table and diagrams bar diagram

For the mid-values 4,8,12,16,20 the first class of the distribution is _________.

  1. 0-8

  2. 1-7

  3. 2-6

  4. none of them
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Mid-values are calculated as (lower limit + upper limit) / 2. For the first class, if the mid-value is 4 and the interval width is 4 (based on the difference between consecutive mid-values), the class is 2-6, where (2+6)/2 = 4.

Multiple choice business maths random variables and probability distribution poisson distribution poisson distrubution probability distributions


 lf the mean is $\lambda$ and the variance is $\sigma^{2}$ in a Poisson distribution, then

  1. $\displaystyle \lambda=\frac{1}{2}\sigma^{2}$
  2. $\displaystyle \sigma^{2}=\frac{1}{2}\lambda$
  3. $\lambda=\sigma^{2}$
  4. $\sigma^{2}=\lambda^{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a Poisson distribution, mean and variance are equal .
i.e.$\lambda = \sigma^2$

Multiple choice business maths random variables and probability distribution poisson distribution poisson distrubution probability distributions

If ${\overline{x}}$ and $\sigma^{2}$ are mean and variance of poisson distribution, then

  1. $\overline{x}>\sigma^{2}$
  2. $\overline{x}<\sigma^{2}$
  3. $\overline{x}=\sigma^{2}$
  4. $\overline{x}+\sigma^{2}=1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a Poisson distribution, mean ($\mu$) and variance ($\sigma^2$ )are equal .
i.e.$\mu = \sigma^2$