Statistics Test

Result

Statistics Test - 51

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Weekly Quiz Competition

Question 1
1 / -0

If $$\sum _{ i=1 }^{ 9 }{ ({ x }_{ i }-5)=9 } $$ and $$\sum _{ i=1 }^{ 9 }{ { { ( }x_{ i }-5 })^{ 2 }=45 }, $$ then the standard deviation of the 9 items $${ x }_{ 1 },{ x }_{ 2, }.........{ x }_{ 9 }$$ is

A
4

B
2

C
3

D
9

Solution
Question 2
1 / -0

The standard deviation of $$50$$ values of a variable x is $$15$$; if each value of the variable is divided by $$(-3)$$; then the standard division of the new set of $$50$$ values of x will be

A
$$15$$

B
$$-15$$

C
$$5$$

D
$$-5$$

Solution
Question 3
1 / -0

mean deviation from mean of the data
marks 10 15 20 25 30
No.of student 2 4 68 5 5

A
5

B
5.2

C
5.12

D
5.5
Question 4
1 / -0

.

A
5

B
5.28

C
6

D
6.29

Solution
Question 5
1 / -0

The variance of $$20$$ observations is $$5 .$$ If each observation is multiplied by $$- 1$$ and added by $$2 ,$$ then new variance is

A
$$-5$$

B
$$5$$

C
$$5.1$$

D
$$7$$

Solution
Question 6
1 / -0

for two data sets,each of size 5, the variances are given to be 4 and 5 andthe correspondings means are given to be 2 and 4 respectively. the variances of the combined data set is

A
11/2

B
6

C
13/2

D
5/2

Solution

Question 7

1 / -0

The mean deviation about the mean of the following data is?

$$x_1$$	3	9	17	23	27
$$f_1$$	8	10	12	9	5

$$5.68$$

$$7.09$$

$$8.69$$

$$8.98$$

Solution

Given data is

$$x_i$$	$$3$$	$$9$$	$$17$$	$$23$$	$$27$$
$$f_i$$	$$8$$	$$10$$	$$12$$	$$9$$	$$5$$

$$x_i$$	$$f_i$$	$$f_ix_i$$	$$\|x_i - \bar{x}\|$$	$$f_i \|x_i - \bar{x}\|$$
$$3$$ $$9$$ $$17$$ $$23$$ $$27$$	$$8$$ $$10$$ $$12$$ $$9$$ $$5$$	$$24$$ $$90$$ $$204$$ $$207$$ $$137$$	$$12$$ $$6$$ $$2$$ $$8$$ $$12$$	$$96$$ $$60$$ $$24$$ $$72$$ $$60$$
	$$N = 44$$	$$\sum f_ix_i = 660$$		$$\sum f_i \|x_i - \bar{x}\| = 312$$

Mean $$\bar{x} = \dfrac{\sum f_i x_i}{N}$$

$$= \dfrac{660}{44}$$

$$\Rightarrow \bar{x} = 15$$

Mean deviation $$= \dfrac{\sum f_i |x_i - \bar{x}|}{N}$$

$$ = \dfrac{312}{44}$$

$$\Rightarrow$$ Mean deviation $$ = 7.09$$.

$$\therefore$$ Mean deviation about mean of the following data is $$7.09$$ is correct answer.

Question 8
1 / -0

If mean deviation through median is 15 and median is 450, then coefficient of mean deviation is

A
$$\dfrac{1}{30}$$

B
30

C
15

D
45

Solution

$$\textbf{Step 1: Apply the Mean Deviation formula.}$$
$$\text{Given: Mean deviation through median}=15$$
$$\text{Median}=450$$
$$\text{Coefficient of Mean Deviation }$$$$= \dfrac{Mean\ deviation\ through\ median}{Median}$$

$$=\dfrac{15}{450}$$

$$=\dfrac{1}{30}$$

$$\textbf{Hence, the coefficient of Mean Deviation is }\dfrac{1}{30}.$$
Question 9
1 / -0

If $$\sum _{ i=1 }^{ 18 }{ } $$ $$(X_{i}-8)=9$$ and $$\sum _{ i=1 }^{ 18 }{ } $$$$(x_{i}-8)^{2}=45$$ , then the standard deviation of $$x_{1},x_{2},.....,x_{18}$$ is

A
4/9

B
9/4

C
3/2

D
2/3

Solution
Question 10
1 / -0

The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is

A
$$\sqrt { \dfrac { 52 }{ 7 } } $$

B
$$\sqrt { 6 } $$

C
$$\dfrac { 52 }{ 7 } $$

D
6

Solution

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Re-Attempt Weekly Quiz Competition

marks	10	15	20	25	30
No.of student	2	4	68	5	5

Statistics Test - 51

Result

Statistics Test - 51

Score

-

Rank

-

SHARING IS CARING

Question 1

4

2

3

9

Solution

Question 2

$$15$$

$$-15$$

$$5$$

$$-5$$

Solution

Question 3

5

5.2

5.12

5.5

Question 4

5

5.28

6

6.29

Solution

Question 5

$$-5$$

$$5$$

$$5.1$$

$$7$$

Solution

Question 6

11/2

6

13/2

5/2

Solution

Question 7

$$5.68$$

$$7.09$$

$$8.69$$

$$8.98$$

Solution

Question 8

$$\dfrac{1}{30}$$

30

15

45

Solution

Question 9

4/9

9/4

3/2

2/3

Solution

Question 10

$$\sqrt { \dfrac { 52 }{ 7 } } $$

$$\sqrt { 6 } $$

$$\dfrac { 52 }{ 7 } $$

6

Solution

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