MCQ Questions for Class 11 Commerce Economics Measures Of Dispersion Quiz 6

The sum of the squares of deviation of 10 observations from their mean 50 is 250, then coefficient of variation is

0%
10%
0%
40%
0%
50%
0%
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

0%
$$\displaystyle \beta=5\alpha $$
0%
$$\displaystyle \beta=4\alpha+3 $$
0%
$$\displaystyle \beta=4\alpha$$
0%
None

Find the mean for the following data using step deviation method.

0%
$$4$$
0%
$$5$$
0%
$$6$$
0%
$$7$$

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.

0%
both (a) and (b) are true
0%
both (a) and (b) are false
0%
(a) is true but (b) is false
0%
(a) is false but (b) is true

Standard deviation is ________.

0%
most widely used measure of dispersion
0%
independent of origin
0%
not independent of scale
0%
all of these

Find the mean for the following data using step deviation method.

0%
$$9$$
0%
$$10$$
0%
$$11$$
0%
$$12$$

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 $$5.4$$

0%
I only
0%
II only
0%
I and II only
0%
I and III only
0%
I, II, and III

Find the mean for the following data using step deviation method.

0%
$$43$$
0%
$$44$$
0%
$$45$$
0%
$$46$$

Find the coefficient of variation.

0%
$$72.66$$
0%
$$81.24$$
0%
$$264$$
0%
$$330$$
0%
None

Which of the following can be used as measures of dispersions?

0%
Range
0%
Percentiles
0%
Standard Deviation
0%
All

The mean of a distribution is $$14$$ and standard deviation is $$5$$. What is the value of the coefficient of variation?

0%
$$57.7\%$$
0%
$$45.7\%$$
0%
$$35.7\%$$
0%
None of these

Find the mean for the following data using step deviation method.

0%
$$15.833$$
0%
$$16.833$$
0%
$$17.833$$
0%
$$18.833$$

A random variable $$X$$ has the probability distribution given below. Its variance is

X	1	2	3	4	5
P(X=x)	k	2k	3k	2k	k

0%
$$\dfrac{16}{3}$$
0%
$$\dfrac{4}{3}$$
0%
$$\dfrac{5}{3}$$
0%
$$\dfrac{10}{3}$$

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

0%
$$12$$
0%
$$0.12$$
0%
$$20$$
0%
$$120$$

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

0%
$$\lambda \sigma$$
0%
$$-\lambda \sigma$$
0%
$$|\lambda| \sigma$$
0%
$${\lambda}^n \sigma$$

Find the variance of the following distribution.

Class interval	$$20-24$$	$$25-29$$	$$30-34$$	$$35-39$$	$$40-44$$	$$45-49$$
Frequency	$$15$$	$$25$$	$$28$$	$$12$$	$$12$$	$$8$$

0%
$$416$$
0%
$$46$$
0%
$$16$$
0%
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

0%
$$30\dfrac{1}{5}$$
0%
$$31\dfrac{1}{3}$$
0%
$$32\dfrac{1}{2}$$
0%
$$33\dfrac{1}{3}$$

If the mean of the numbers $$a,b,8,5,10$$ is $$6$$ and their variance is $$68$$, then $$ab$$ is equal to

0%
$$6$$
0%
$$7$$
0%
$$12$$
0%
$$14$$
0%
$$25$$

If $$n=10, \bar{x}=12$$ and $$\sum x^2=1530$$, then calculate the coefficient of variation.

0%
$$20$$
0%
$$25$$
0%
$$30$$
0%
$$35$$

Calculate the standard deviation of the following data.

x	$$3$$	$$8$$	$$13$$	$$18$$	$$23$$
f	$$7$$	$$10$$	$$15$$	$$10$$	$$8$$

0%
$$6.32$$.
0%
$$2.32$$.
0%
$$3.32$$.
0%
None of these

Calculate the standard deviation of the following data.
$$10, 20, 15, 8, 3, 4$$

0%
$$5.97$$
0%
$$59.7$$
0%
$$4.97$$
0%
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 ?

0%
1 only
0%
2 only
0%
Both 1 and 2
0%
Neither 1 nor 2

The arithmetic mean of the observations 10,8,5,a,b is 6 and their variance 6.Then ab=

0%
6
0%
4
0%
3
0%
12

If the standard deviation is small, we define a new variable known as ________.

0%
student's F-distribution
0%
student's T-variable
0%
chi-square distribution
0%
student's G-variable

Coefficient of quartile deviation of numbers $$6, 8, 9, 10, 11, 12, 14$$ is?

0%
$$1/5$$
0%
$$1/10$$
0%
$$2/5$$
0%
$$1/4$$

Which of the following are measures of dispersion?

0%
Standard Deviation,Median,Range
0%
Standard Deviation,Mode,Range
0%
Standard Deviation,Variance,Range
0%
Mean,Mode,Median

What are the objectives of measure of dispersion?

0%
Helpful in use of further statistical analysis as in regression, correlation etc.
0%
Reliability of measure of central tendency
0%
Control of variability
0%
All of the above

Which of the following are measures of central tendency.

0%
Percentile, Quartile, Median
0%
Median,Mode, Percentile
0%
Percentile, Quartile, Mode
0%
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.

0%
$$31.26$$
0%
$$30.06$$
0%
$$29.142$$
0%
$$27.85$$

The formula of standard error of sample mean is ________.

0%
$$\dfrac{\sqrt{PQ}}{\sqrt{n}}$$
0%
$$\dfrac{\sigma}{\sqrt{n}}$$
0%
$$\dfrac{\sqrt{N-n}}{\sqrt{N-1}}$$
0%
$$\dfrac{\sqrt{N}}{\sigma}$$

$$X_i$$	$$F_i$$	$$d=\cfrac{X-A}{i}$$	$$F_i d_i$$
2	10	-1	-10
4=A	20	0	0
6	30	1	30
8	40	2	80
	$$\Sigma f = 100$$		$$\Sigma fd = 100$$

X	F	$$d=\cfrac{X-A}{i}$$	Fd
3	5	-1	-5
6=A	10	-0	-0
9	15	1	15
12	20	2	40
	$$\Sigma f = 50$$		$$\Sigma fd = 50$$

X	F	$$d=\cfrac{x-A}{i} $$	Fd
12=A	1	0	0
24	2	1	2
36	3	2	6
48	4	3	12
60	5	4	20
	$$\Sigma f = 15$$		$$\Sigma fd = 40$$

X	C. I. mid point	F	$$d=\cfrac{X-A}{i}$$	Fd
0-5	2.5	4	-1	-4
5-10	7.5=A	8	0	0
10-15	12.5	12	1	12
15-20	17.5	16	2	32
20-25	22.5	20	3	60
		$$\Sigma F = 60$$		$$\Sigma Fd=100$$

$$Class$$	$$Mid-point$$ $$(x)$$	$$Frequency$$ $$(f)$$	$$xf$$	$$(x-\overline{x})$$	$$(x-\overline{x})^2$$	$$(x-\overline{x})^2f$$
$$20-24$$	$$22$$	$$15$$	$$330$$	$$-10.25$$	$$105.0625$$	$$1575.9375$$
$$25-29$$	$$27$$	$$25$$	$$675$$	$$-5.25$$	$$27.5625$$	$$689.0625$$
$$30-34$$	$$32$$	$$28$$	$$896$$	$$-0.25$$	$$0.0625$$	$$1.75$$
$$35-39$$	$$37$$	$$12$$	$$444$$	$$4.75$$	$$22.5625$$	$$270.75$$
$$40-44$$	$$42$$	$$12$$	$$504$$	$$9.75$$	$$95.0625$$	$$1140.75$$
$$45-49$$	$$47$$	$$8$$	$$376$$	$$14.75$$	$$217.5625$$	$$1740.5$$
		$$\sum f=100$$	$$\sum xf=3225$$			$$\sum(x-\overline{x})^2f=5418.75$$

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

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Practice Class 11 Commerce Economics Quiz Questions and Answers

$$x$$	$$f$$	$$xf$$	$$(x-\overline{x})$$	$$(x-\overline{x})^2$$	$$(x-\overline{x})^2f$$
$$3$$	$$7$$	$$21$$	$$-10.2$$	$$104.04$$	$$728.28$$
$$8$$	$$10$$	$$80$$	$$-5.2$$	$$27.04$$	$$270.4$$
$$13$$	$$15$$	$$195$$	$$-0.2$$	$$0.04$$	$$0.6$$
$$18$$	$$10$$	$$180$$	$$4.8$$	$$23.04$$	$$230.4$$
$$23$$	$$8$$	$$184$$	$$9.8$$	$$96.04$$	$$768.32$$
	$$\sum f=50$$	$$\sum xf=660$$			$$\sum(x-\overline{x})^2=1998$$

$$X$$	$$X-\overline{X}$$	$$(X-\overline{X})^2$$
$$3$$	$$-7$$	$$49$$
$$4$$	$$-6$$	$$36$$
$$8$$	$$-2$$	$$4$$
$$10$$	$$0$$	$$0$$
$$15$$	$$5$$	$$25$$
$$20$$	$$10$$	$$100$$
		$$\sum (X-\overline{X})^2=214$$

$$x$$	$$\|x-M\|$$
$$06$$	$$60$$
$$13$$	$$53$$
$$54$$	$$12$$
$$66$$	$$0$$
$$89$$	$$23$$
$$91$$	$$25$$
$$97$$	$$31$$
	$$\sum \|x-M\|=204$$

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

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Practice Class 11 Commerce Economics Quiz Questions and Answers

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