Statistics Test

Result

Statistics Test - 49

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Weekly Quiz Competition

Question 1
1 / -0

Standard deviation of $$3, 5, 7, 9, 11, 13$$ is?

A
$$12$$

B
$$11$$

C
$$11.66$$

D
None
Question 2
1 / -0

The variance of first $$20$$- natural numbers is?

A
$$\dfrac{399}{4}$$

B
$$\dfrac{379}{12}$$

C
$$\dfrac{133}{2}$$

D
$$\dfrac{133}{4}$$

Solution

$$Var[X]=E[X^{2}]-(E[X])^{2}=\cfrac{1}{20}[(1^{2}+2^{2}+.....+20^{2})]-(E[X])^{2}$$
Now, $$E[X]=\sum_{i=1}^{20}P_{i}X_{i}=\cfrac{1}{20}(1+2+3+...+20)=10.5$$
$$(P_{1}=P_{2}=P_{3}=.......P_{20}=\cfrac{1}{20})$$
$$\therefore Var[X]=\cfrac{1}{20}[(1^{2}+2^{2}+3^{2}+....+20^{2})]-10.5^{2}=\cfrac{1}{20}\times 2870-110.25$$
$$=143.5-110.25=33.25=\cfrac{133}{4}$$
Question 3
1 / -0

In an experiment with $$10$$ observations on $$x,\displaystyle \sum { x=60, } \displaystyle \sum { { x }^{ 2 } } =1000$$ one observation that was $$20$$ was found to be wrong and was replaced by the correct value $$30$$ then the correct variance is

A
$$64$$

B
$$111$$

C
$$52$$

D
$$101$$
Question 4
1 / -0

Variance of the data given below
Size of item 3.5 4.5 5.5 6.5 7.5 8.5 9.5
Frequency 3 7 22 60 85 32 8

A
1

B
1.231

C
1.321

D
1.312

Solution
Question 5
1 / -0

For a series the information available is $$n=10$$, $$\displaystyle\sum x=60, \displaystyle\sum x^2=1000$$. The standard deviation is?

A
$$8$$

B
$$64$$

C
$$24$$

D
$$128$$
Question 6
1 / -0

The standard deviation of $$15$$ terms is $$6$$ and each item is decreased by $$1$$. Then the standard deviation of new data is?

A
$$5$$

B
$$7$$

C
$$\dfrac{91}{15}$$

D
$$6$$

Solution

If each term of the data set is increased or decreased by the same amount, the standard deviation remains unchanged.
$$\therefore$$ Standard deviation of the new data set is also 6.
.
Question 7
1 / -0

For r.v. X whose p.m.f. is
X 0 1 2
p(X=)x $${ b }^{ 2 }$$ 2ab $${ a }^{ 2 }$$
Std. deviation of $$X i.e.\sigma =$$

A
$$\sqrt { ab } $$

B
$$\sqrt { 2ab } $$

C
$$\sqrt { 3ab } $$

D
$$2\sqrt { ab } $$
Question 8
1 / -0

The standard deviation of $$1, 2, 3, 4, 5, 6, 7$$ is?

A
$$4$$

B
$$2$$

C
$$\sqrt{7}$$

D
None of the above

Solution

Given observation is
$$1,2,3,4,6,7$$
Mean=$$\cfrac { 1+2+3+4+5+6+7 }{ 7 } =\cfrac { 28 }{ 7 } =4$$
Variance=$$\sum _{ +r=1 }^{ n }{ \cfrac { \left( x-{ x }_{ i } \right) ^{ 2 } }{ n } } =\cfrac { \left( 1-4 \right) ^{ 2 }+\left( 2-4 \right) ^{ 2 }+\left( 3-4 \right) ^{ 2 }+\left( 4-4 \right) ^{ 2 }+\left( 5-4 \right) ^{ 2 }+\left( 6-4 \right) ^{ 2 }+\left( 7-4 \right) ^{ 2 } }{ 7 } \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad =\cfrac { { 3 }^{ 2 }+{ 2 }^{ 2 }+{ 1 }^{ 2 }+0+{ 1 }^{ 2 }+{ 2 }^{ 2 }+{ 3 }^{ 2 } }{ 7 } \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad =\cfrac { 9+4+1+1+4+9 }{ 7 } =\cfrac { 28 }{ 7 } =4$$
standard deviation=$$\sqrt { variance } \\ \sqrt { 4 } =2$$
Question 9
1 / -0

If the variance of the data 2,4,5,6,8,17 is 23,33, then variance of 5,11,14,17,23,50 is ________________.

A
46,66

B
96.32

C
209,97

D
213,97
Question 10
1 / -0

In a series of $$100$$ observations, half of them is equal to $$p$$ and remaining half equal to $$-p$$ if the standard deviation of these observations is $$10$$ then $$|p|=$$__

A
$$10$$

B
$$\dfrac {1}{10}$$

C
$$\dfrac {1}{\sqrt {10}}$$

D
$$\sqrt {10}$$

Solution

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Re-Attempt Weekly Quiz Competition

Size of item	3.5	4.5	5.5	6.5	7.5	8.5	9.5
Frequency	3	7	22	60	85	32	8

X	0	1	2
p(X=)x	$${ b }^{ 2 }$$	2ab	$${ a }^{ 2 }$$

Statistics Test - 49

Result

Statistics Test - 49

Score

-

Rank

-

SHARING IS CARING

Question 1

$$12$$

$$11$$

$$11.66$$

None

Question 2

$$\dfrac{399}{4}$$

$$\dfrac{379}{12}$$

$$\dfrac{133}{2}$$

$$\dfrac{133}{4}$$

Solution

Question 3

$$64$$

$$111$$

$$52$$

$$101$$

Question 4

1

1.231

1.321

1.312

Solution

Question 5

$$8$$

$$64$$

$$24$$

$$128$$

Question 6

$$5$$

$$7$$

$$\dfrac{91}{15}$$

$$6$$

Solution

Question 7

$$\sqrt { ab } $$

$$\sqrt { 2ab } $$

$$\sqrt { 3ab } $$

$$2\sqrt { ab } $$

Question 8

$$4$$

$$2$$

$$\sqrt{7}$$

None of the above

Solution

Question 9

46,66

96.32

209,97

213,97

Question 10

$$10$$

$$\dfrac {1}{10}$$

$$\dfrac {1}{\sqrt {10}}$$

$$\sqrt {10}$$

Solution

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