CBSE Questions for Class 11 Commerce Economics Measures Of Dispersion Quiz 6 - MCQExams.com

The sum of the squares of deviation of 10 observations from their mean 50 is 250, then coefficient of variation is
  • 10%
  • 40%
  • 50%
  • none of these
Consider the following groups A and B
A : 3, 4, 5,...... upto n terms
B : 15, 19, 23,..... upto n terms
If the mean deviations of groups A and B about their means are $$\displaystyle \alpha \: \: \: and\: \: \: \beta  $$ respectively then
  • $$\displaystyle \beta=5\alpha $$
  • $$\displaystyle \beta=4\alpha+3 $$
  • $$\displaystyle \beta=4\alpha$$
  • None
Find the mean for the following data using step deviation method.
453076.png
  • $$4$$
  • $$5$$
  • $$6$$
  • $$7$$
Which of the following are true or false?
a) T-distribution varies from+infinity to-infinity.
b)The variance of t distribution and the variance of normal distribution become closer and closer as the size of the sample increases.
  • both (a) and (b) are true
  • both (a) and (b) are false
  • (a) is true but (b) is false
  • (a) is false but (b) is true
Standard deviation is ________.
  • most widely used measure of dispersion
  • independent of origin
  • not independent of scale
  • all of these
Find the mean for the following data using step deviation method.
453078.png
  • $$9$$
  • $$10$$
  • $$11$$
  • $$12$$
The mean of a finite set X of numbers is $$14$$, the median of this set of numbers is $$12$$, and the standard deviation is $$1.8$$. A new set Y is formed by multiplying each member of the set S by $$3$$. Determine the correct statements w.r.t. set Y:
I. The mean of the numbers is set Y is $$42$$
II. The median of the numbers in set Y is $$36$$
III. The standard deviation of the numbers is set Y is $$5.4$$
  • I only
  • II only
  • I and II only
  • I and III only
  • I, II, and III
Find the mean for the following data using step deviation method.
453080.png
  • $$43$$
  • $$44$$
  • $$45$$
  • $$46$$
Find the coefficient of variation.
  • $$72.66$$
  • $$81.24$$
  • $$264$$
  • $$330$$
  • None
Which of the following can be used as measures of dispersions?
  • Range
  • Percentiles
  • Standard Deviation
  • All
The mean of a distribution is $$14$$ and standard deviation is $$5$$. What is the value of the coefficient of variation?
  • $$57.7\%$$
  • $$45.7\%$$
  • $$35.7\%$$
  • None of these
Find the mean for the following data using step deviation method.
453084.png
  • $$15.833$$
  • $$16.833$$
  • $$17.833$$
  • $$18.833$$
A random variable $$X$$ has the probability distribution given below. Its variance is 
X12345
P(X=x)k2k3k2kk
  • $$\dfrac{16}{3}$$
  • $$\dfrac{4}{3}$$
  • $$\dfrac{5}{3}$$
  • $$\dfrac{10}{3}$$
If the standard deviation of a set of scores is $$1.2$$ and their mean is $$10$$, then the coefficient of variation of the scores is
  • $$12$$
  • $$0.12$$
  • $$20$$
  • $$120$$
Standard Deviation of n observations $$a_1, a_2, a_3 .....a_n$$ is $$\sigma$$ Then the standard deviation of the observations $$\lambda a_1, \lambda a_2, ..., \lambda a_n$$ is
  • $$\lambda \sigma$$
  • $$-\lambda \sigma$$
  • $$|\lambda| \sigma$$
  • $${\lambda}^n \sigma$$
Find the variance of the following distribution.
Class interval
$$20-24$$
$$25-29$$
$$30-34$$
$$35-39$$
$$40-44$$
$$45-49$$
Frequency
$$15$$
$$25$$
$$28$$
$$12$$
$$12$$
$$8$$
  • $$416$$
  • $$46$$
  • $$16$$
  • None of these
If the median of the data 6,7,x-2,x,18,21 written in ascending order is 16, then the variance of that data is 
  • $$30\dfrac{1}{5}$$
  • $$31\dfrac{1}{3}$$
  • $$32\dfrac{1}{2}$$
  • $$33\dfrac{1}{3}$$
If the mean of the numbers $$a,b,8,5,10$$ is $$6$$ and their variance is $$68$$, then $$ab$$ is equal to
  • $$6$$
  • $$7$$
  • $$12$$
  • $$14$$
  • $$25$$
If $$n=10, \bar{x}=12$$ and $$\sum x^2=1530$$, then calculate the coefficient of variation.
  • $$20$$
  • $$25$$
  • $$30$$
  • $$35$$
Calculate the standard deviation of the following data.
x
$$3$$
$$8$$
$$13$$
$$18$$
$$23$$
f
$$7$$
$$10$$
$$15$$
$$10$$
$$8$$
  • $$6.32$$.
  • $$2.32$$.
  • $$3.32$$.
  • None of these
Calculate the standard deviation of the following data.
$$10, 20, 15, 8, 3, 4$$
  • $$5.97$$
  • $$59.7$$
  • $$4.97$$
  • None of these
Let X denote the number of scores which exceed 4 in 1 toss of a symmetrical die. Consider the following statements :
The arithmetic mean of X is
The standard deviation of X is
Which of the above statements is/are correct ?
  • 1 only
  • 2 only
  • Both 1 and 2
  • Neither 1 nor 2
The arithmetic mean of the observations 10,8,5,a,b is 6 and their variance 6.Then ab=
  • 6
  • 4
  • 3
  • 12
If the standard deviation is small, we define a new variable known as ________.
  • student's F-distribution
  • student's T-variable
  • chi-square distribution
  • student's G-variable
Coefficient of quartile deviation of numbers $$6, 8, 9, 10, 11, 12, 14$$ is?
  • $$1/5$$
  • $$1/10$$
  • $$2/5$$
  • $$1/4$$
Which of the following are measures of dispersion?
  • Standard Deviation,Median,Range
  • Standard Deviation,Mode,Range
  • Standard Deviation,Variance,Range
  • Mean,Mode,Median
What are the objectives of measure of dispersion?
  • Helpful in use of further statistical analysis as in regression, correlation etc.
  • Reliability of measure of central tendency
  • Control of variability
  • All of the above
Which of the following are measures of central tendency.
  • Percentile, Quartile, Median
  • Median,Mode, Percentile
  • Percentile, Quartile, Mode
  • Mean,Mode, Median

The runs scored by Virat in 7 different matches are given as:

                 $$89,91,54,66,13,97,06$$

Calculate the mean deviation about the median for this data.

  • $$31.26$$
  • $$30.06$$
  • $$29.142$$
  • $$27.85$$
The formula of standard error of sample mean is ________.
  • $$\dfrac{\sqrt{PQ}}{\sqrt{n}}$$
  • $$\dfrac{\sigma}{\sqrt{n}}$$
  • $$\dfrac{\sqrt{N-n}}{\sqrt{N-1}}$$
  • $$\dfrac{\sqrt{N}}{\sigma}$$
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