Statistics Test

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Statistics Test - 42

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Weekly Quiz Competition

Question 1
1 / -0

A group of $$50$$ house owners contributes money towards children's education of their street. The amount of money collected is shown in the table below: (use direct method).

A
Rs. $$27$$

B
Rs. $$17$$

C
Rs. $$10$$

D
Rs. $$23$$

Solution

Answer:- Given $$\Sigma f=50$$
Using frequency distribution table

Amount No. of house owners $$x_i$$ $$x_i f_i$$
0-10 5 5 25
10-20 10 15 150
20-30 15 25 375
30-40 10 35 350
40-50 10 45 450
$$\Sigma f_i=50$$ $$\Sigma f_i x_i = 1350$$
$$\therefore$$ Amount of money collected = Arithmetic mean
$$\Rightarrow \; Mean = \cfrac{\Sigma f_i x_i}{\Sigma f_i} = \cfrac{1350}{50}=27$$
$$\therefore \; $$ the amount of money collected = 27Rs.
A) Rs. 27
Question 2
1 / -0

Calculate the average income of workers .

A
$$10$$ rupees

B
$$9$$ rupees

C
$$8$$ rupees

D
$$7$$ rupees

Solution

Arithmetic mean using direct method formula is $$\bar { x } = \dfrac { \sum { { f }_{ i }{ x }_{ i } } }{ \sum { { f }_{ i } } } $$
$$\bar { x } = \dfrac { 28,600 }{ 3,200 } $$
$$\bar { x } = 8.93\sim 9$$ rupees.
Therefore, the mean of the number of children is approximately $$9$$ rupees.
Question 3
1 / -0

Find the arithmetic mean of the following table using direct method.

A
$$30$$ min

B
$$50 $$ min

C
$$35 $$ min

D
$$40 $$ min

Solution

Arithmetic mean using direct method formula is $$\bar { x } = \dfrac { \sum { { f }_{ i }{ x }_{ i } } }{ \sum { { f }_{ i } } } $$
$$\bar { x } = \dfrac { 35,000 }{ 1,000 } $$ min
$$\bar { x } = 35 $$ min
Question 4
1 / -0

Calculate the mean of the number of children of frequency .

A
$$30$$

B
$$20$$

C
$$10$$

D
$$40$$

Solution

Arithmetic mean using direct method formula is $$\bar { x } = \dfrac { \sum { { f }_{ i }{ x }_{ i } } }{ \sum { { f }_{ i } } } $$
$$\bar { x } = \dfrac { 1,041 }{ 35 } $$
$$\bar { x } = 29.74 \sim 30$$.
Therefore, the mean of the number of children is approximately $$30$$.
Question 5
1 / -0

Calculate arithmetic mean using direct method for the following data shows distance covered by $$50$$ persons to perform their work inside the factory.

A
$$20.5 km$$

B
$$32.8 km$$

C
$$25.2 km$$

D
$$27.6 km$$

Solution

Answer:- Using direct method
Representing the data into frequency distribution table
$$x_i =\text{mid point of each class interval}$$

Class interval No. of workers
$$(f_i)$$ $$x_i$$ $$f_i x_i$$
1-11 4 6 24
11-21 6 16 96
21-31 10 26 260
31-41 12 36 432
41-51 18 46 828
$$\Sigma f_i=50$$ $$\Sigma f_ix_i=1640$$
$$\therefore \; mean = \cfrac{\Sigma f_ix_i}{\Sigma f_i} =\cfrac{1640}{50}=32.8$$
Average distance covered by 50 persons = 32.8
B)32.8

Question 6

1 / -0

Calculate arithmetic mean using direct method for the following data shows distance covered by $$125$$ buses to perform its duty.

$$23.1\ km$$

$$30.5\ km$$

$$23.6\ km$$

$$34.2\ km$$

Solution

Answer:- Using direct method

Representing the data into frequency distribution table

Distance $$(x_i)$$	No. of buses $$(f_i)$$	$$f_ix_i$$
$$50$$	$$5$$	$$ 250$$
$$ 45$$	$$15$$	$$675$$
$$35$$	$$25$$	$$ 875$$
$$20$$	$$35$$	$$700$$
$$10$$	$$45$$	$$450$$
	$$\Sigma f_i=125$$	$$\Sigma f_i x_i =2950$$

$$\therefore \; mean = \cfrac{\Sigma f_ix_i}{\Sigma f_i} =\cfrac{2950}{125} = 23.6$$

$$\therefore$$ The distance covered by $$25$$ buses is $$23.6\ km$$

Question 7
1 / -0

Joshua's mark obtained for each subject is given below. Find the average mark

A
$$90$$

B
$$91$$

C
$$94$$

D
$$92$$

Solution

Answer:- Using direct method

Marks obtained
$$x_i$$ No. of students
$$f_i$$ $$f_i x_i$$
90 3 270
92 1 92
95 2 190
86 4 344
96 5 480

$$\Sigma f_i = 15$$ $$\Sigma f_i x_i = 1376$$
Mean = $$\cfrac{\Sigma f_i x_i}{\Sigma f_i} = \cfrac{1376}{15} = 92$$
D) 92
Question 8
1 / -0

Find the mean height of $$30$$ players using direct method:

A
$$151 cm$$

B
$$149 cm$$

C
$$148 cm$$

D
$$150 cm$$

Solution

Answer:- Using direct method

Height (in cm)
$$x_i$$ No. of Players
$$f_i$$ $$f_i x_i$$
100 3 300
120 6 720
150 2 300
160 5 800
170 10 1700
180 4 720
$$\Sigma f_i = 30$$ $$\Sigma f_i x_i = 4540$$
Mean = $$\cfrac{\Sigma f_i x_i}{\Sigma f_i} = \cfrac{4540}{30} = 151.33 \simeq 151$$
Average height is 151 cm.
A)151

Question 9

1 / -0

Number of dog's	2-4	4-6	6-8	8-10
weight (kg)	20	10	12	15

Find the arithmetic mean of dog's weight using direct method.

$$5.17$$ kg

$$4.56$$ kg

$$5.77$$ kg

$$4.58$$ kg

Solution

Number of dog's	Weight (kg) $$(f_i)$$	Midpoint $$(X_i)$$	$$f_iX_i$$
2-4	20	3	$$20\times 3=60$$
4-6	10	5	$$10\times 5=50$$
6-8	12	7	$$12\times 7=84$$
8-10	15	9	$$15\times 9=135$$
	$$\sum f_i = 57$$		$$\sum f_ix_i = 329$$

Arithmetic mean using direct method formula is $$\bar { x } = \dfrac { \sum { { f }_{ i }{ x }_{ i } } }{ \sum { { f }_{ i } } } $$
$$\bar { x } = \dfrac { 329 }{ 57 } $$
$$\bar { x } = 5.77$$
The average mean weight of the dog is $$5.77 kg$$.

Question 10
1 / -0

Find the mean height of $$100$$ trees:

A
$$74$$ m

B
$$70$$ m

C
$$71$$ m

D
$$72$$ m

Solution

Arithmetic mean using direct method formula is $$\bar { x } = \dfrac { \sum { { f }_{ i }{ x }_{ i } } }{ \sum { { f }_{ i } } } $$
$$\bar { x } = \dfrac { 7,360 }{ 100 } $$
$$\bar { x } = 73.60$$.
Therefore, the average height is approximately $$74 $$ m.

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Amount	No. of house owners	$$x_i$$	$$x_i f_i$$
0-10	5	5	25
10-20	10	15	150
20-30	15	25	375
30-40	10	35	350
40-50	10	45	450
	$$\Sigma f_i=50$$		$$\Sigma f_i x_i = 1350$$

Class interval	No. of workers $$(f_i)$$	$$x_i$$	$$f_i x_i$$
1-11	4	6	24
11-21	6	16	96
21-31	10	26	260
31-41	12	36	432
41-51	18	46	828
	$$\Sigma f_i=50$$		$$\Sigma f_ix_i=1640$$

Marks obtained $$x_i$$	No. of students $$f_i$$	$$f_i x_i$$
90	3	270
92	1	92
95	2	190
86	4	344
96	5	480

	$$\Sigma f_i = 15$$	$$\Sigma f_i x_i = 1376$$

Height (in cm) $$x_i$$	No. of Players $$f_i$$	$$f_i x_i$$
100	3	300
120	6	720
150	2	300
160	5	800
170	10	1700
180	4	720
	$$\Sigma f_i = 30$$	$$\Sigma f_i x_i = 4540$$

Statistics Test - 42

Result

Statistics Test - 42

Score

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Rank

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SHARING IS CARING

Question 1

Rs. $$27$$

Rs. $$17$$

Rs. $$10$$

Rs. $$23$$

Solution

Question 2

$$10$$ rupees

$$9$$ rupees

$$8$$ rupees

$$7$$ rupees

Solution

Question 3

$$30$$ min

$$50 $$ min

$$35 $$ min

$$40 $$ min

Solution

Question 4

$$30$$

$$20$$

$$10$$

$$40$$

Solution

Question 5

$$20.5 km$$

$$32.8 km$$

$$25.2 km$$

$$27.6 km$$

Solution

Question 6

$$23.1\ km$$

$$30.5\ km$$

$$23.6\ km$$

$$34.2\ km$$

Solution

Question 7

$$90$$

$$91$$

$$94$$

$$92$$

Solution

Question 8

$$151 cm$$

$$149 cm$$

$$148 cm$$

$$150 cm$$

Solution

Question 9

$$5.17$$ kg

$$4.56$$ kg

$$5.77$$ kg

$$4.58$$ kg

Solution

Question 10

$$74$$ m

$$70$$ m

$$71$$ m

$$72$$ m

Solution

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