Statistics Test

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Statistics Test - 43

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Question 1
1 / -0

For the observations $${ x }_{ 1, }{ x }_{ 2 },{ x }_{ 3 },........{ x }_{ 18, }$$ it is given that $$\sum _{i =1 }^{ 18 }{ ({ x }_{ i }-8)=9 } $$ and $$\sum _{ j=1}^{ 18 }{ { ({ x }_{ j}-8) }^{ 2 }=45 } $$ then the standard deviation of these eighteen observations is

A
$$\cfrac { 3 }{ 2 } $$

B
5

C
$$\cfrac { 5 }{ \sqrt { 2 } } $$

D
$$\sqrt { \cfrac { 81 }{ 34 } } $$

Solution
Question 2
1 / -0

Directions For Questions

The daily wages (in $$Rs$$) of $$11$$ persons given as $$140, 145, 130, 165, 160, 125, 150, 170, 175, 120, 180$$ then

...view full instructions

the coefficient of quartile deviation is

A
$$\dfrac{40}{3}$$

B
$$\dfrac{15}{2}$$

C
$$20$$

D
$$150$$

Solution

$$\begin{array}{l} 120,125,130,140,145,150,160,165,170,175,180 \\ n=11 \\ \Rightarrow { Q_{ 1 } }=\left( { \frac { { n+1 } }{ 4 } } \right) th\, \, term=\left( { \frac { { 12 } }{ 4 } } \right) th\, \, term=3th\, \, term \\ \Rightarrow { Q_{ 3 } }=130 \\ and \\ { Q_{ 3 } }=3\left( { \frac { { n+1 } }{ 4 } } \right) th\, \, term\, =3\left( { \frac { { 12 } }{ 4 } } \right) th\, \, term=9th\, \, term=170 \\ Then,\, \, coefficient\, \, of\, \, quartiledeviation\, \, =\frac { { \left( { { Q_{ 3 } }-{ Q_{ 1 } } } \right) } }{ { \left( { { Q_{ 3 } }+{ Q_{ 1 } } } \right) } } \times 100 \\ =100\times \frac { { \left( { 170-130 } \right) } }{ { \left( { 170+130 } \right) } } =\frac { { 40 } }{ { 300 } } \times 100=\frac { { 40 } }{ 3 } \, \, \end{array}$$
Question 3
1 / -0

Mode of the data $$3,2,3,2,3,5,6,6,5,3,2,5$$ is

A
$$3$$

B
$$2$$

C
$$5$$

D
$$6$$
Question 4
1 / -0

The variance of the elements of the row which contains $$2019$$ is $$K$$ then the value of $$3 K$$ is

A
$$2024$$

B
$$2000$$

C
$$1800$$

D
$$1024$$
Question 5
1 / -0

The variance of first $$30$$ natural numbers, is

A
$$74.92$$

B
$$37.98$$

C
$$38.98$$

D
$$none\ of\ these$$

Solution

We know that the variance of first $$n$$ natural number is
$$= \cfrac { { { n^{ 2 } }-1 } }{ { 12 } } $$

Put $$ n=30$$

Therefore,
$$ \\ \cfrac { { 900-1 } }{ { 12 } } =\cfrac { { 899 } }{ { 12 } } \\ =74.916 \\ =74.92$$

Hence, this is the answer.
Question 6
1 / -0

If the mean deviation about the median of the numbers $$a,2a,....,50a$$ is $$50$$, then $$|a|$$ equals:-

A
$$4$$

B
$$5$$

C
$$2$$

D
$$3$$

Solution

Given series:- $$a, 2a, 3a, ....., 50a$$
Median $$= \cfrac{25a + 26a}{2} = 25.5 a$$
Mean deviation about median $$= 50 \quad \left( \text{Given} \right)$$
Mean deviation $$= \cfrac{\sum_{i = 1}^{50}{\left| {x}_{i} - 25.5a \right|}}{50}$$
$$\therefore \cfrac{24.5a + 23.5a + 22.5a + ..... + 23.5a + 24.5a}{50} = 50$$
$$\Rightarrow a + 3a + 5a + ..... + 47a + 49a = 2500$$
$$\Rightarrow \cfrac{25}{2} \left( 2a + \left( 25 - 1 \right) 2a \right) = 2500$$
$$\Rightarrow 2a \times 25 = 200$$
$$\Rightarrow a = \cfrac{200}{50} = 4$$
Question 7
1 / -0

The variance of first $$50$$ even natural numbers is:-

A
$$833$$

B
$$831$$

C
$$438$$

D
$$\dfrac {437}{4}$$
Question 8
1 / -0

Two distributions each of $$5$$ observations having veriance $$4$$ and $$5$$. If their arithmetic mean are $$2$$ and $$4$$ respectively., Find the variance of combined distribution

A
$$5/2$$

B
$$11/2$$

C
$$6$$

D
$$13/2$$

Solution
Question 9
1 / -0

.

A
5

B
4

C
6

D
7
Question 10
1 / -0

If $$\displaystyle\sum _{ i=1 }^{ 18 }{ \left( { x }_{ i }-8 \right) } =153,\displaystyle\sum _{ i=1 }^{ 18 }{ \left( { x }_{ i }-8 \right) ^{ 2 } } =45$$ then standard deviation of $$x_{1},x_{2},........,x_{n}$$ is

A
$$4/9$$

B
$$9/4$$

C
$$3/2$$

D
$$2/3$$

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Re-Attempt Weekly Quiz Competition

Statistics Test - 43

Result

Statistics Test - 43

Score

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SHARING IS CARING

Question 1

$$\cfrac { 3 }{ 2 } $$

5

$$\cfrac { 5 }{ \sqrt { 2 } } $$

$$\sqrt { \cfrac { 81 }{ 34 } } $$

Solution

Question 2

$$\dfrac{40}{3}$$

$$\dfrac{15}{2}$$

$$20$$

$$150$$

Solution

Question 3

$$3$$

$$2$$

$$5$$

$$6$$

Question 4

$$2024$$

$$2000$$

$$1800$$

$$1024$$

Question 5

$$74.92$$

$$37.98$$

$$38.98$$

$$none\ of\ these$$

Solution

Question 6

$$4$$

$$5$$

$$2$$

$$3$$

Solution

Question 7

$$833$$

$$831$$

$$438$$

$$\dfrac {437}{4}$$

Question 8

$$5/2$$

$$11/2$$

$$6$$

$$13/2$$

Solution

Question 9

5

4

6

7

Question 10

$$4/9$$

$$9/4$$

$$3/2$$

$$2/3$$

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