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 shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

The standard deviation $\sigma$ of the first $N$ natural numbers can be obtained using which one of the following formula?

  1. $\sigma =\cfrac { { N }^{ 2 }-1 }{ 12 } $
  2. $\sigma =\sqrt { \cfrac { { N }^{ 2 }-1 }{ 12 } } $
  3. $\sigma =\sqrt { \cfrac { N-1 }{ 12 } } $
  4. $\sigma =\sqrt { \cfrac { { N }^{ 2 }-1 }{ 6N } } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\sigma^2=\dfrac{1}{n}\sum _{i=1}^{n}i^2-\left(\dfrac{1}{n}\sum _{i=1}^{n}i\right)^2$


     $=\dfrac{1}{n}(1^2+2^2+...+n^2)-\left(\dfrac{1}{n}(1+2+...+n)\right)^2$

     $=\dfrac{1}{n} \times \dfrac{n(n+1)(2n+1)}{6}-(\dfrac{n+1}{2})^2=\dfrac{n^2-1}{12}$

$\therefore \sigma=\sqrt{\dfrac{n^2-1}{12}}$

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

A researcher has collected the following sample data. The mean of the sample is 5.
3  5  12  3  2
The standard deviation is...............

  1. 8.944

  2. 4.062

  3. 13.2

  4. 16.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Data: 3, 5, 12, 3, 2. Mean = (3+5+12+3+2)/5 = 25/5 = 5. Variance = [(3-5)^2 + (5-5)^2 + (12-5)^2 + (3-5)^2 + (2-5)^2] / 5 = [4 + 0 + 49 + 4 + 9] / 5 = 66 / 5 = 13.2. SD = sqrt(13.2) = 3.63. If using sample SD (divide by n-1=4), Variance = 66/4 = 16.5, SD = sqrt(16.5) = 4.062.

Multiple choice book keeping and accountancy accounting equation meaning, objectives and need of adjustments need for adjustments accounting equations and transactions

A shopkeeper wants to stock shoes. The best suitable average for him will be?

  1. Arithmetic mean

  2. Median

  3. Mode

  4. Geometric mean
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The mode represents the most frequently occurring value in a dataset. A shoe shopkeeper needs to know which shoe size is sold the most to restock efficiently, making mode the most suitable average.

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

If the period of variations is more than one year, then the variations are termed as __________.

  1. Random variations

  2. Cyclical variations

  3. Seasonal variations

  4. (b) or (c)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cyclical variations are long-term fluctuations in a time series that occur over a period longer than one year, often associated with business cycles (booms and recessions).

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

Examples of infinite population__________.

  1. the stars in the sky and the cars in a town

  2. the stars in the sky and the books in a library

  3. the cars in a town and the books in a library

  4. output from a machine and births of insect
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Infinite population refers to the population that cannot be calculated easily i.e. they are unlimited in size. Example : births of insect, as one cannot calculate the birth of insects easily.

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 physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

The random error in the arithmetic mean of 100 observations is x, then random error in the arithmetic mean of 400 observation would be

  1. 4x
  2. $\dfrac { 1 }{ 4 } x$

  3. 2x
  4. $\dfrac { 1 }{ 2 } x$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The random error in the mean of n observations is inversely proportional to the square root of n. When the number of observations increases from 100 to 400 (a factor of 4), the error decreases by a factor of sqrt(4) = 2, making the new error x / 2.