Quantitative Aptitude

Statistics

606 Questions
All Ungrouped data dispersion and consistency 209 Unknown terms from given average 124 Grouped data central tendencies 101 Merging means and variances of groups 53 Replacement change in average 27 Alligation and weighted average 21 Data interpretation from tables and charts 20 Net successive percentage change 19 Grouped data variance via step deviation 18 Combination of multiple ratios 1

Statistics 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 C.V of a distribution is $80\%$ and the mean of the distribution is $40$, the S.D of the distribution is ________.

  1. $33$
  2. $32$
  3. $35$
  4. $0.30$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Coefficient of variation is the coefficient of dispersion based on the standard deviation of the statistical series.

Coefficient of variation = ( standard deviation / mean )

=> 80 /100 = S.D / 40 

=> S.D = 32 

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

For a distribution, coefficient of variation is 22.5% and mean is 7.5 find the standard deviation___.

  1. 1.9975

  2. 1.6875

  3. 1.243

  4. 1.0943
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Coefficient of Variation (CV) = (SD / Mean) * 100. Given CV = 22.5% and Mean = 7.5, then 22.5 = (SD / 7.5) * 100. SD = (22.5 * 7.5) / 100 = 168.75 / 100 = 1.6875.

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

Two years ago the mean age of $40$ people was $11$ years. Now a person left the group and the mean age is changed to $12$ years, then the age of the person who left the group is?

  1. $52$ years
  2. $48$ years
  3. $54$ years

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

Sum of ages 2 years ago = 40*11 = 440. Sum of ages now = 440 + 40*2 = 520. After one person leaves, 39 people have mean age 12, sum = 39*12 = 468. Age of person = 520 - 468 = 52.

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.

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 ${ \mu  } _{ 2 }=20,{ \mu  } _{ 2 }^{ 1 }=276$ for a discrete random variable $X$, then the mean of the random variable $X$ is

  1. $16$
  2. $5$
  3. $2$
  4. $1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\mu _2=E(X^2)-[E(X)]^2......(i)$

$\mu _2'=E(X)^2.....(ii)$
Given: $\mu _2=20, \mu _2'=276$
from equation (ii) $\implies E(x^2)=276$
and from equation (i), $\implies 20=276-[E(X)]^2$
$\implies [E(X)]^2=276-20=250\\implies E(X)=16$
is the mean of random variable.

Multiple choice maths average arithmetic mean of ap introduction to averages means

If each observation is multiplied by $\displaystyle \frac{1}{3}$ then the mean of the new data will de

  1. $\displaystyle \frac{1}{3}$ times

  2. 3 times
  3. $\displaystyle \frac{1}{\sqrt{3}}$ times
  4. $\displaystyle \frac{2}{3}$ times
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let set of data is 9,10,11,17 and 13

Then mean =$\frac{9+10+11+17+13}{5}=\frac{60}{5}$
If Each observation is multiply by $\frac{9+10+11+17+13}{5}=\frac{60}{5}=12$
Then data are $\frac{9}{3},\frac{10}{3},\frac{11}{3},\frac{17}{3}and \frac{13}{3}$
Then sum of data=$\frac{9}{3}+\frac{10}{3}+\frac{11}{3}+\frac{17}{3}+ \frac{13}{3}=\frac{60}{3}=20$
Then new mean of data=$\frac{20}{5}=4$
Then new data mean =$\frac{4}{12}=\frac{1}{3}$ times of old data

Multiple choice maths average arithmetic mean of ap introduction to averages means

Mean deviation of first $7$ natural no. about their A.M. is?

  1. $2$
  2. $\sqrt{2}$
  3. $\dfrac{12}{7}$
  4. $0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The first 7 natural numbers are 1, 2, 3, 4, 5, 6, 7. Their arithmetic mean (A.M.) is (1+2+3+4+5+6+7)/7 = 28/7 = 4. The absolute deviations from the mean 4 are |1-4|, |2-4|, |3-4|, |4-4|, |5-4|, |6-4|, |7-4|, which are 3, 2, 1, 0, 1, 2, 3. The sum of these deviations is 3+2+1+0+1+2+3 = 12. The mean deviation is therefore 12/7.

Multiple choice maths average arithmetic mean of ap introduction to averages means

Coefficient of variance of a distribution is 60% and the standard deviation is 25. The arithmetic mean of the distribution is

  1. $\cfrac {25}{3}$

  2. 35
  3. $\cfrac {125}{3}$
  4. $\cfrac {25}{6}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The coefficient of variation (CV) is given by (Standard Deviation / Mean) * 100. Rearranging the formula for the mean gives Mean = (Standard Deviation / CV) * 100 = (25 / 60) * 100 = 125 / 3.

Multiple choice maths average arithmetic mean of ap introduction to averages means

The mean of $3$ observations is $12$ and mean of $5$ observations is $4$ the combined mean is 

  1. 7

  2. 8

  3. 9

  4. 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The no .of  observations is $3+5=8$

The sum of observations is $3(12)+5(4)=36+20=56$
The mean is $\dfrac{56}{8}=7$