Measures of Dispersion Test

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Measures of Dispersion Test - 15

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Weekly Quiz Competition

Question 1
1 / -0

The middle value of an ordered series is called _______.

A
$$2nd$$ quartile

B
$$5th$$ decile

C
$$50th$$ percentile

D
All the above
Question 2
1 / -0

Directions For Questions

The following table gives the distribution of daily wages of $$900$$ workers. However, the frequencies of the two classes $$40-50$$ and $$60-70$$ are missing. If the median of the distribution is Rs. $$59.25$$, find the missing figures.

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Class Intervals $$30-40$$ $$40-50$$ $$50-60$$ $$60-70$$ $$70-80$$
Frequency $$120$$ ? $$200$$ ? $$185$$
Cumulative Frequency $$120$$ ? ? ? $$900$$
Cumulative Frequency for class $$60-70=$$?

A
$$715$$

B
$$465$$

C
$$145$$

D
$$265$$

Solution

Class Intervals Wages Frequency(f) Cumulative Frequency
$$30-40$$ $$120$$ $$120$$
$$40-50$$ $$f_1$$ $$120+f_1$$
$$50-60$$ $$200$$ $$320+f_1$$
$$60-70$$ $$f_2$$ $$320+f_1+f_2$$
$$70-80$$ $$185$$ $$900$$
Since median is given to be $$59.25$$, the median class is $$50-60$$. Thus, we can write, Solving this for $$f_1$$ we get, $$f_1=145$$; Further $$f_2=900-(120+145+200+185)=250$$.
Question 3
1 / -0

Extreme value have no effect on _______.

A
average

B
median

C
geometric mean

D
harmonic mean
Question 4
1 / -0

Paasche Price Index Number = ?

A
$$220.00$$

B
$$216.30$$

C
$$219.12$$

D
$$221.98$$

Solution

Paasche Price Index Number
$$P^{p}_{01} =\dfrac{\Sigma P_{1}Q_{1}}{\Sigma P_{0}Q_{1}} \times {100} = \dfrac{398}{184}\times {100} = 216.30$$.
Question 5
1 / -0

Find the present value of Rs. $$10,000$$ to be required after $$5$$ years if the interest rate be $$9\%$$. Given that $$(1.09)^5=1.5386$$.

A
$$6,994.42$$

B
$$6,949.24$$

C
$$6,449.24$$

D
$$6,499.42$$

Solution

Here, $$i=0.09=9\%$$
$$n=5$$
$$A_n=10,000$$
Required present value $$=\displaystyle\frac{A_n}{(1+i)^n}$$
$$=\displaystyle\frac{10,000}{(1+0.09)^5}$$
$$=Rs. 6499.42$$.

Question 6

1 / -0

Calculate standard deviation of the following data.

X	$$0-10$$	$$10-20$$	$$20-30$$	$$30-40$$	$$40-50$$
f	$$10$$	$$8$$	$$15$$	$$8$$	$$4$$

$$-12$$

$$12$$

$$12.36$$

$$152.77$$

Solution

Marks	Mid-values(X)	f	dxi$$=X-25/10$$	$$fdx_if$$	$$dx_i^2$$
$$0-10$$	$$5$$	$$10$$	$$-2$$	$$-20$$	$$40$$
$$10-20$$	$$15$$	$$8$$	$$-1$$	$$-8$$	$$8$$
$$20-30$$	$$25$$	$$15$$	$$0$$	$$0$$	$$0$$
$$30-40$$	$$35$$	$$8$$	$$1$$	$$8$$	$$8$$
$$40-50$$	$$45$$	$$4$$	$$2$$	$$8$$	$$16$$
Total		$$45$$		$$-12$$	$$72$$

$$\sqrt{\displaystyle\frac{72}{45}-\frac{144}{45\times 45}}\times 10$$
$$=12.36$$

Question 7

1 / -0

Calculate standard deviation of the following data.

X	$$10$$	$$11$$	$$12$$	$$13$$	$$14$$	$$15$$	$$16$$	$$17$$	$$18$$
f	$$2$$	$$7$$	$$10$$	$$12$$	$$15$$	$$11$$	$$10$$	$$6$$	$$3$$

$$3.95$$

$$1.99$$

$$14$$

None of the above

Solution

X	f	fx	X-Mean	$$f(X-x)^2$$
$$10$$	$$2$$	$$20$$	$$-4$$	$$32$$
$$11$$	$$7$$	$$77$$	$$-3$$	$$63$$
$$12$$	$$10$$	$$120$$	$$-2$$	$$40$$
$$13$$	$$12$$	$$156$$	$$-11$$	$$2$$
$$14$$	$$15$$	$$210$$	$$0$$	$$0$$
$$15$$	$$11$$	$$165$$	$$1$$	$$11$$
$$16$$	$$10$$	$$160$$	$$2$$	$$40$$
$$17$$	$$6$$	$$102$$	$$3$$	$$54$$
$$18$$	$$3$$	$$54$$	$$4$$	$$48$$
Total	$$76$$	$$fX=1064$$		$$f(X-X)^2=300$$

$$^-{X}=\displaystyle\frac{1064}{76}=14$$
$$\sigma x=\sqrt{\displaystyle\frac{300}{76}}$$
$$=\sqrt{3.95}$$
$$=1.99$$.

Question 8
1 / -0

Y bought a CD Player costing Rs. $$13,000$$ by making a down payment of Rs. $$3,000$$ and agreeing to make equal annual payment for four years. How much would be each payment if the interest on unpaid amount be $$14\%$$ compounded annually?$$[P(4, 0.14)2.91371]$$

A
Rs. $$3,432.05$$

B
Rs. $$3,423.50$$

C
Rs. $$3,342.05$$

D
Rs. $$3,234.50$$

Solution

V$$=$$A.P(n, i)
Here $$n=4$$ and $$i=0.14$$
$$=\displaystyle\frac{10,000}{P(4, 0.14)}$$
$$[P(20, 0.10)=8.51356$$ from table $$2$$(a)]
$$=\displaystyle\frac{10,000}{2.91371}$$
$$=$$Rs. $$3,432.05$$. Therefore each payment would be Rs. $$3,432.05$$.
Question 9
1 / -0

The mean and standard deviation of $$10$$ observations are $$35$$ and $$2$$ respectively. Find the changed mean and standard deviation if each observation is increased by $$4$$.

A
$$39$$ & $$6$$

B
$$2$$ & $$39$$

C
$$39$$ & $$2$$

D
$$6$$ & $$39$$

Solution

When each observation is increased by $$4$$, the mean of the changed observations will also increase and it will become equal to $$35+4=39$$.
Since increment in all observations by a constant does not change the standard deviation. Thus, the mean and standard deviation when each observation is increased by $$4$$ would be $$39$$ and $$2$$ respectively.
Question 10
1 / -0

Paasche Price Index = ?

A
$$157.33$$

B
$$153.14$$

C
$$153.33$$

D
$$157.14$$

Solution

Paasche Price Index Number
$$P^{P}_{01} =\dfrac{\Sigma P_{1}Q_{1}}{\Sigma P_{0}Q_{1}} \times {100} = \dfrac{22}{14}\times{100} = 157.14$$.

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Class Intervals	$$30-40$$	$$40-50$$	$$50-60$$	$$60-70$$	$$70-80$$
Frequency	$$120$$	?	$$200$$	?	$$185$$
Cumulative Frequency	$$120$$	?	?	?	$$900$$

Class Intervals Wages	Frequency(f)	Cumulative Frequency
$$30-40$$	$$120$$	$$120$$
$$40-50$$	$$f_1$$	$$120+f_1$$
$$50-60$$	$$200$$	$$320+f_1$$
$$60-70$$	$$f_2$$	$$320+f_1+f_2$$
$$70-80$$	$$185$$	$$900$$

Measures of Dispersion Test - 15

Result

Measures of Dispersion Test - 15

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SHARING IS CARING

Question 1

$$2nd$$ quartile

$$5th$$ decile

$$50th$$ percentile

All the above

Question 2

$$715$$

$$465$$

$$145$$

$$265$$

Solution

Question 3

average

median

geometric mean

harmonic mean

Question 4

$$220.00$$

$$216.30$$

$$219.12$$

$$221.98$$

Solution

Question 5

$$6,994.42$$

$$6,949.24$$

$$6,449.24$$

$$6,499.42$$

Solution

Question 6

$$-12$$

$$12$$

$$12.36$$

$$152.77$$

Solution

Question 7

$$3.95$$

$$1.99$$

$$14$$

None of the above

Solution

Question 8

Rs. $$3,432.05$$

Rs. $$3,423.50$$

Rs. $$3,342.05$$

Rs. $$3,234.50$$

Solution

Question 9

$$39$$ & $$6$$

$$2$$ & $$39$$

$$39$$ & $$2$$

$$6$$ & $$39$$

Solution

Question 10

$$157.33$$

$$153.14$$

$$153.33$$

$$157.14$$

Solution

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