Descriptive Statistics Test 50

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Descriptive Statistics Test 50

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Weekly Quiz Competition

Question 1
1 / -0

Choose the correct answer from the alternatives given.
Directions for questions 71 to 75: Study the following bar-graph and answer the questions.
The average electric consumption by the family during these 5 months in 2013 is

A
470 units

B
440 units

C
450 units

D
460 units

Solution

Average units consumption in the year 2013
$$\displaystyle = \, \frac{550 \, + \, 500 \, + \, 400 \, + \, 350 \, + \, 500}{5} \, = \frac{2300}{5}$$ = $$460$$ units
Question 2
1 / -0

Choose the correct answer from the alternatives given.
Directions for questions 71 to 75: Study the following bar-graph and answer the questions.
For how many months in 2012, the consumption of electric units was more than the average units consumption?

A
3

B
2

C
5

D
4

Solution

Average units consumption in the year 2012
$$\displaystyle \frac{600 \, + \, 700 \, + \, 400 \, + \, 300 \, + \, 200}{5} \, = \, \frac{2200}{5}$$ = 440 units
Hence, required months are July and August.
Question 3
1 / -0

If the sum of mean and variance of $$B.D$$ for $$5$$ trials is $$1.8$$, the binomial distribution is

A
$$ (0.8+0.2)^5$$

B
$$ (0.2+1.8)^5$$

C
$${\left( {0.8 + 0.2} \right)^{10}}$$

D
$${\left( {0.2 + 1.8} \right)^{10}}$$

Solution

a binomial distribution is characterized by $$2$$ parameters:
$$n$$ - number of trials
$$p$$ - probability of success in one trail.
We there by know n=5, we need to find $$p$$ .
$$Mean$$ of the binomial distribution is given by,
$$mean = np$$
variance is given by

$$variance\quad =\quad np(1-p)\\ \therefore \quad mean\quad +\quad variance\quad =\quad 1.8\\ =>\quad 5p\quad +\quad 5p(1-p)\quad =\quad 1.8\\ =>\quad 5{ p }^{ 2 }-10p+1.8=0\\ =>\quad p=\quad 0.2\quad or\quad 1.8$$
$$ =>\quad p=\quad 0.2\ [\because 1\ge p\ge 0]$$
$$q=0.8$$
Binomial distribution is $$(0.2+0.8)^n$$.
Hence the answer is A
Question 4
1 / -0

Variance of $$^{10}C_{0}, ^{10}C_{1}, ^{10}C_{2},^{10}C_{10}$$ is:

A
$$\dfrac{10.^{20}C_{10}-2^{10}}{100}$$

B
$$\dfrac{11.^{20}C_{10}-2^{10}}{11}$$

C
$$\dfrac{10.^{20}C_{10}-2^{20}}{100}$$

D
$$\dfrac{10.^{20}C_{10}-2^{10}}{121}$$
Question 5
1 / -0

What is standard deviation of the set of observations $$32,28,29,30,31$$?

A
$$1.6$$

B
$$\sqrt { 2 }$$

C
$$2$$

D
$$none\ of\ these$$

Solution

$$\sigma =\displaystyle \sum _{ i=1 }^{ n }{ \sqrt { \dfrac { \left( { x }_{ i }-{ x }_{ av } \right) }{ m-1 } } } $$
$${ x }_{ au }=\dfrac { 32+28+29+30+31 }{ 5 } =30$$
$$\therefore =\sqrt { \dfrac { { \left( 32-30 \right) }^{ 2 }+{ \left( 28-30 \right) }^{ 2 }+{ \left( 29-30 \right) }^{ 2 }+{ \left( 30-30 \right) }^{ 2 }+{ \left( 31-30 \right) }^{ 2 } }{ 5-1 } } $$
$$=\sqrt { \dfrac { 4+4+1+1 }{ 4 } } =\sqrt { \dfrac { 10 }{ 4 } } =\sqrt { \dfrac { 10 }{ 2 } } =1.58$$
Question 6
1 / -0

Directions For Questions

Percentage of steel by different companies in three consecutive years(in lakh tones)

...view full instructions

Study the following graph carefully and answer the question given.
Which of the following companies recorded the minimum percentage growth from $$1994$$ to $$1995$$?

A
A

B
B

C
C

D
F

Solution

order of company growth from $$1994$$ to $$1995$$ is
$$E<A<B<C<F<D$$
Question 7
1 / -0

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

A
$$12$$

B
$$11$$

C
$$11.66$$

D
None
Question 8
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 9
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 10
1 / -0

Standard deviation of the first $$2$$n + $$1$$ natural numbers is

A
$$\sqrt{\dfrac {n(n+1)}{2}}$$

B
$$\sqrt{\dfrac {n(n+1)(2n + 1)}{3}}$$

C
$$\sqrt{\dfrac {n(n+1)}{3}}$$

D
$$\sqrt{\dfrac {n^2(n+1)}{2}}$$

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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

Descriptive Statistics Test 50

Result

Descriptive Statistics Test 50

Score

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Rank

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SHARING IS CARING

Question 1

470 units

440 units

450 units

460 units

Solution

Question 2

3

2

5

4

Solution

Question 3

$$ (0.8+0.2)^5$$

$$ (0.2+1.8)^5$$

$${\left( {0.8 + 0.2} \right)^{10}}$$

$${\left( {0.2 + 1.8} \right)^{10}}$$

Solution

Question 4

$$\dfrac{10.^{20}C_{10}-2^{10}}{100}$$

$$\dfrac{11.^{20}C_{10}-2^{10}}{11}$$

$$\dfrac{10.^{20}C_{10}-2^{20}}{100}$$

$$\dfrac{10.^{20}C_{10}-2^{10}}{121}$$

Question 5

$$1.6$$

$$\sqrt { 2 }$$

$$2$$

$$none\ of\ these$$

Solution

Question 6

A

B

C

F

Solution

Question 7

$$12$$

$$11$$

$$11.66$$

None

Question 8

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

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

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

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

Solution

Question 9

1

1.231

1.321

1.312

Solution

Question 10

$$\sqrt{\dfrac {n(n+1)}{2}}$$

$$\sqrt{\dfrac {n(n+1)(2n + 1)}{3}}$$

$$\sqrt{\dfrac {n(n+1)}{3}}$$

$$\sqrt{\dfrac {n^2(n+1)}{2}}$$

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