Descriptive Statistics Test 51

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Descriptive Statistics Test 51

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Weekly Quiz Competition

Question 1
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 2
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 3
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 4
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 5
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 6
1 / -0

$$\sum _{ i=1 }^{ 10 }{ { \left( { X }_{ i }-10 \right) }^{ 2 }=2000 } \sum _{ i=1 }^{ 10 }{ { X }_{ i }-10 } =100$$ then the standard deviation of data set $${X}_{i}$$.

A
$$1$$

B
$$5$$

C
$$10$$

D
$$2$$
Question 7
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 8
1 / -0

Find the standard deviation of 10 observation 111, 211, 311,.......,1011.

A
100$$\sqrt { 3 } $$

B
250

C
300

D
50$$\sqrt { 33 } $$
Question 9
1 / -0

The mean and standard deviation of $$1,2,3,4,5,6$$ are

A
$$\dfrac{7}{2},\sqrt{\dfrac{35}{12}}$$

B
$$\dfrac{7}{3} ,\sqrt{3}$$

C
$$3,3$$

D
$$3,35/12$$

Solution
Question 10
1 / -0

The average marks of 10 students in a class is 60 with standard deviation 4 while the average marks of other 10 students is 40 with standard deviation 6. If all the 20 students are taken together, their standard deviation will be

A
$$\sqrt {109}$$

B
12

C
$$\sqrt {116}$$

D
$$\sqrt {126}$$

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

Descriptive Statistics Test 51

Result

Descriptive Statistics Test 51

Score

-

Rank

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SHARING IS CARING

Question 1

$$8$$

$$64$$

$$24$$

$$128$$

Question 2

$$5$$

$$7$$

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

$$6$$

Solution

Question 3

$$\sqrt { ab } $$

$$\sqrt { 2ab } $$

$$\sqrt { 3ab } $$

$$2\sqrt { ab } $$

Question 4

$$4$$

$$2$$

$$\sqrt{7}$$

None of the above

Solution

Question 5

46,66

96.32

209,97

213,97

Question 6

$$1$$

$$5$$

$$10$$

$$2$$

Question 7

$$64$$

$$111$$

$$52$$

$$101$$

Question 8

100$$\sqrt { 3 } $$

250

300

50$$\sqrt { 33 } $$

Question 9

$$\dfrac{7}{2},\sqrt{\dfrac{35}{12}}$$

$$\dfrac{7}{3} ,\sqrt{3}$$

$$3,3$$

$$3,35/12$$

Solution

Question 10

$$\sqrt {109}$$

12

$$\sqrt {116}$$

$$\sqrt {126}$$

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