Descriptive Statistics Test 44

Result

Descriptive Statistics Test 44

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Weekly Quiz Competition

Question 1
1 / -0

Let $$\sigma^{2}$$ is variance of following frequency distribution
$$x_{1}$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$
$$f_{1}$$ $$1$$ $$0$$ $$1$$ $$7$$ $$9$$ $$4$$ $$1$$ $$1$$ $$1$$
then $$\sigma^{2}$$ is equal to

A
$$2.4$$

B
$$2.5$$

C
$$2.6$$

D
$$2.7$$
Question 2
1 / -0

The mean and variance of a random variable having a binomial distribution are $$4$$ and $$2$$ respectively , then $$P(X=1)$$ is

A
$$1/32$$

B
$$1/16$$

C
$$1/8$$

D
$$1/4$$

Solution
Question 3
1 / -0

Let $$x_i$$ represents the outcome on a fair die and $$f_i$$ be the corresponding frequency. The variance for random variable $$x_i$$ with following frequency distribution, is
$$x_i$$ 1 2 3 4 5 6
$$f_i$$ 1 2 3 4 5 6

A
$$2$$

B
$$3$$

C
$$\dfrac{28}{9}$$

D
$$\dfrac{20}{9}$$
Question 4
1 / -0

The mean and the standard devition (s.d) of five observations are $$9$$ and $$0$$, respecively. If one of the observations is changed such that the mean of the new set of five obervatons becomes $$10$$, then their s. d. is:

A
0

B
1

C
2

D
4

Solution

Since the standard deviation before the change was $$0$$, all the observation was the mean, or $$9$$. Since one observation was changed and the new mean is $$10$$, we have the following equation.

$$ \dfrac{9+9+9+9+x}{5}=10 $$

$$ \Rightarrow \dfrac{36+x}{5}=10 $$

$$ \Rightarrow 36+x=50 $$

$$ \Rightarrow x=14 $$

The changed observation is$$14$$ .

All the observations are$$\left\{ 9,9,9,9,14 \right\}$$

Since the mean is $$10$$,

The variance is

$$ \dfrac{\left[ {{\left( 9-10 \right)}^{2}}+{{\left( 9-10 \right)}^{2}}+{{\left( 9-10 \right)}^{2}}+{{\left( 9-10 \right)}^{2}}{{\left( 14-10 \right)}^{2}} \right]}{5} $$

$$ \Rightarrow \dfrac{\left( 1+1+1+1+16 \right)}{5} $$

$$ \Rightarrow 4 $$

Hence, the standard deviation is $$\sqrt{4}=2$$
Question 5
1 / -0

Let $$x_{1},\ x_{2},...x_{100}$$ are $$100$$ above observation such that $$\displaystyle \sum { { x }_{ 1 }=0 } ,\ \displaystyle \sum _{ 1\le i<j\le 100 }^{ }{ \left| { x }_{ i }{ x }_{ j } \right| =80000 } $$ & mean deviation from their mean is $$5$$, then their standard deviation, is-

A
$$10$$

B
$$30$$

C
$$40$$

D
$$50$$
Question 6
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 7
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 8
1 / -0

If the sum and sum of squares of $$10$$ observations are $$12$$ and $$18$$ resp., then, The $$S.D$$ of observations is :-

A
$$\dfrac{1}{5}$$

B
$$\dfrac{2}{5}$$

C
$$\dfrac{3}{5}$$

D
$$\dfrac{4}{5}$$

Solution

$$\sum x=12,\sum x^2=18,N=10$$
$$SD=\sqrt{\cfrac{\sum x^2}{N}-(\cfrac{\sum x}{N})^2}$$
$$\implies SD=\sqrt{\cfrac{18}{10}-(\cfrac{12}{10})^2}=\cfrac{3}{5}$$
Question 9
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 10
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.

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Re-Attempt Weekly Quiz Competition

$$x_{1}$$	$$1$$	$$2$$	$$3$$	$$4$$	$$5$$	$$6$$	$$7$$	$$8$$	$$9$$
$$f_{1}$$	$$1$$	$$0$$	$$1$$	$$7$$	$$9$$	$$4$$	$$1$$	$$1$$	$$1$$

$$x_i$$	1	2	3	4	5	6
$$f_i$$	1	2	3	4	5	6

Descriptive Statistics Test 44

Result

Descriptive Statistics Test 44

Score

-

Rank

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SHARING IS CARING

Question 1

$$2.4$$

$$2.5$$

$$2.6$$

$$2.7$$

Question 2

$$1/32$$

$$1/16$$

$$1/8$$

$$1/4$$

Solution

Question 3

$$2$$

$$3$$

$$\dfrac{28}{9}$$

$$\dfrac{20}{9}$$

Question 4

0

1

2

4

Solution

Question 5

$$10$$

$$30$$

$$40$$

$$50$$

Question 6

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

5

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

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

Solution

Question 7

$$5/2$$

$$11/2$$

$$6$$

$$13/2$$

Solution

Question 8

$$\dfrac{1}{5}$$

$$\dfrac{2}{5}$$

$$\dfrac{3}{5}$$

$$\dfrac{4}{5}$$

Solution

Question 9

$$2024$$

$$2000$$

$$1800$$

$$1024$$

Question 10

$$74.92$$

$$37.98$$

$$38.98$$

$$none\ of\ these$$

Solution

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