Statistics Test

Result

Statistics Test - 41

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Weekly Quiz Competition

Question 1

1 / -0

Find the arithmetic mean using direct method for the following data shows distance covered by $$120$$ passengers to perform their regular work.

$$20\ km$$

$$25\ km$$

$$22\ km$$

$$15\ km$$

Solution

Answer:- Using direct method

Distance	No. of passengers $$f_i$$	$$x_i$$	$$f_i x_i$$
$$5-15$$	$$30$$	$$10$$	$$300$$
$$15-20$$	$$20$$	$$17.5$$	$$350$$
$$20-35$$	$$ 30$$	$$27.5$$	$$825$$
$$35-40$$	$$40$$	$$37.5$$	$$1500$$
	$$\Sigma f_i = 120$$		$$\Sigma f_i x_i = 2975$$

Arithmetic mean $$=\cfrac{\Sigma f_i x_i}{\Sigma f_i} =\cfrac{2975}{120} = 24.79 \simeq 25\ km$$

Question 2
1 / -0

If the average of the following data is $$100$$. Find the value of $$p$$.

A
$$-26$$

B
$$-28$$

C
$$-25$$

D
$$-24$$

Solution

Answer:- Given:- $$\overline {x}=100$$
Using frequency distribution table

x f xf
10 2 20
20 4 80
30 p 30p
40 8 320
50 10 500
60 12 720
$$\Sigma f_i = 36+p$$ $$\Sigma x_i f_i = 1640+30p$$
Average = $$\cfrac{\Sigma fx}{\Sigma f}$$
$$\Rightarrow \; \overline{x} = \cfrac{1640+30p}{36+p}$$
$$\Rightarrow \; 100=\cfrac{1640+30p}{36+p}$$
$$\Rightarrow \; 100(36+p) = 1640+30p$$
$$\Rightarrow \; 3600 + 100p = 1640 + 30p$$
$$\Rightarrow \; 100p-30p = 1640 - 3600$$
$$\Rightarrow \; 70p = -1960$$
$$\Rightarrow \; p=-\cfrac{1960}{70}$$
$$\Rightarrow \; p=-28 $$
B) -28
Question 3
1 / -0

The time(s) taken by a group of students to walk across their college is given in the table below. Find the average time

A
$$12.02 sec$$

B
$$39.12 sec$$

C
$$40.20 sec$$

D
$$31.90 sec$$

Solution

Answer:- Using direct method
Representing the data into frequency distribution table

time
$$(x_i)$$ No. of students
$$(f_i)$$ $$f_ix_i$$
10 1 10
20 2 40
25 5 125
30 6 180
45 7 315
$$\Sigma f_i=21$$ $$\Sigma f_i x_i =670$$
$$\therefore \; mean = \cfrac{\Sigma f_ix_i}{\Sigma f_i} =\cfrac{670}{21}=31.90 sec$$
Average time is 31.90
B) 31.90 sec
Question 4
1 / -0

Find the arithmetic mean for the table given below

A
$$14.18$$

B
$$12.54$$

C
$$13.72$$

D
$$15.61$$

Solution

Answer:-

$$X_i$$ $$f_i$$ $$X_i f_i$$
25 3 75
10 5 50
12 6 72
15 2 30
$$\Sigma f_i=16$$ $$\Sigma f_i x_i=227$$
$$\therefore \;Mean= \cfrac {\Sigma f_i x_i}{\Sigma f_i}=\cfrac {227}{16} = 14.18$$
Question 5
1 / -0

Find the mean of the following frequency distribution using direct method.

A
$$16.20$$

B
$$14.16$$

C
$$16.17$$

D
$$14.28$$

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
$$(f_i)$$ $$x_i$$ $$f_i x_i$$
0-5 4 2.5 10
5-10 5 7.5 37.5
10-15 6 12.5 75
15-20 7 17.5 122.5
20-25 8 22.5 180
$$\Sigma f_i=30$$ $$\Sigma f_ix_i=425$$
$$\therefore \; mean = \cfrac{\Sigma f_ix_i}{\Sigma f_i} =\cfrac{425}{30}=14.16$$
Question 6
1 / -0

The marks scored by two students $$M, N$$ in a class are given below. Find the mean .

A
65 marks

B
70 marks

C
85 marks

D
90 marks

Solution

Answer:- Using direct method
Using frequency distribution table

M
(x) N
(f) fx
98 50 4900
88 65 5720
87 80 6960
90 95 8550
70 100 7000
$$\Sigma f=390$$ $$\Sigma fx=33130$$
$$\therefore \; \text{Average or mean} =\cfrac{\Sigma fx}{\Sigma f}=\cfrac{33130}{390}=84.94 \simeq 85$$
The mean is 85.
C)85 Marks

Question 7

1 / -0

A survey was conducted by a group of students in which they collected the following data regarding the number of plants in $$30$$ houses in a locality. Find the mean number of plants per house.

$$23.4$$

$$25.4$$

$$22.4$$

$$26.4$$

Solution

Given:-

Total no. of houses $$,\Sigma f_i = 30$$

Representing the data in frequency distribution table

No. of plants	No. of houses $$(f_i)$$	Classmark $$(x_i)$$	$$f_i x_i$$
$$0-6$$	$$4$$	$$3$$	$$ 12$$
$$ 6-12$$	$$6$$	$$9$$	$$54$$
$$12-18$$	$$1$$	$$15$$	$$15$$
$$18-24$$	$$3$$	$$21$$	$$63$$
$$24-30$$	$$5$$	$$27$$	$$135$$
$$30-36$$	$$6$$	$$33$$	$$198$$
$$36-42$$	$$5$$	$$39$$	$$195$$
	$$\Sigma f_i=30$$		$$\Sigma f_i x_i = 672$$

$$\therefore \; mean=\cfrac{\Sigma f_i x_i}{\Sigma f_i}=\cfrac{672}{30} = 22.4$$

Hence, the mean no. of plants per house $$= 22.4$$

Question 8
1 / -0

Find the arithmetic mean of the following data.

A
$$253.6$$

B
$$253.75$$

C
$$223.6$$

D
$$243.75$$

Solution

Let us first construct the table.
$$\bar { x } = \dfrac { \sum { { f }_{ i }{ x }_{ i } } }{ \sum { { f }_{ i } } } $$
$$\bar { x } = \dfrac { 6090 }{ 24 } $$
$$\bar { x } = 253.75$$.
Question 9
1 / -0

Farm Size $$56$$ $$57$$ $$58$$ $$59$$ $$60$$ $$61$$ $$62$$
Number of cultivating house holds $$6$$ $$4$$ $$3$$ $$2$$ $$13$$ $$11$$ $$3$$
Find the arithmetic mean of the following data.

A
$$59.35$$

B
$$57.35$$

C
$$61.35$$

D
$$52.35$$

Solution

Let us first construct the table
$$\bar { x } = \dfrac { \sum { { f }_{ i }{ x }_{ i } } }{ \sum { { f }_{ i } } } $$
$$\bar { x } = \dfrac { 2493 }{ 42 } $$
$$\bar { x } = 59.35$$

Question 10

1 / -0

Walmart supermarket recorded the length of time, to the nearest hour, that a sample of $$100$$ cars was parked in their lot. Estimate the average hour using direct method.

$$20$$ hours

$$31$$ hours

$$25$$ hours

$$27$$ hours

Solution

Answer:-

Representing the data into frequency distribution table.

Daily Pocket allowance	No. of workers	$$x_i$$	$$f_i x_i$$
5-15	20	10	200
15-25	30	20	600
25-35	15	30	450
35-45	12	40	480
45-55	6	50	300
55-65	17	60	1020

	$$\Sigma f_i=100$$		$$\Sigma f_i x_i = 3050$$

$$\therefore \; Mean=\cfrac{\Sigma f_i x_i}{\Sigma f_i}=\cfrac{3050}{100}=30.5 \simeq 31$$

The average hours are 31.

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x	f	xf
10	2	20
20	4	80
30	p	30p
40	8	320
50	10	500
60	12	720
	$$\Sigma f_i = 36+p$$	$$\Sigma x_i f_i = 1640+30p$$

time $$(x_i)$$	No. of students $$(f_i)$$	$$f_ix_i$$
10	1	10
20	2	40
25	5	125
30	6	180
45	7	315
	$$\Sigma f_i=21$$	$$\Sigma f_i x_i =670$$

$$X_i$$	$$f_i$$	$$X_i f_i$$
25	3	75
10	5	50
12	6	72
15	2	30
	$$\Sigma f_i=16$$	$$\Sigma f_i x_i=227$$

Class interval	No. of workers $$(f_i)$$	$$x_i$$	$$f_i x_i$$
0-5	4	2.5	10
5-10	5	7.5	37.5
10-15	6	12.5	75
15-20	7	17.5	122.5
20-25	8	22.5	180
	$$\Sigma f_i=30$$		$$\Sigma f_ix_i=425$$

M (x)	N (f)	fx
98	50	4900
88	65	5720
87	80	6960
90	95	8550
70	100	7000
	$$\Sigma f=390$$	$$\Sigma fx=33130$$

Farm Size	$$56$$	$$57$$	$$58$$	$$59$$	$$60$$	$$61$$	$$62$$
Number of cultivating house holds	$$6$$	$$4$$	$$3$$	$$2$$	$$13$$	$$11$$	$$3$$

Statistics Test - 41

Result

Statistics Test - 41

Score

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Rank

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Question 1

$$20\ km$$

$$25\ km$$

$$22\ km$$

$$15\ km$$

Solution

Question 2

$$-26$$

$$-28$$

$$-25$$

$$-24$$

Solution

Question 3

$$12.02 sec$$

$$39.12 sec$$

$$40.20 sec$$

$$31.90 sec$$

Solution

Question 4

$$14.18$$

$$12.54$$

$$13.72$$

$$15.61$$

Solution

Question 5

$$16.20$$

$$14.16$$

$$16.17$$

$$14.28$$

Solution

Question 6

65 marks

70 marks

85 marks

90 marks

Solution

Question 7

$$23.4$$

$$25.4$$

$$22.4$$

$$26.4$$

Solution

Question 8

$$253.6$$

$$253.75$$

$$223.6$$

$$243.75$$

Solution

Question 9

$$59.35$$

$$57.35$$

$$61.35$$

$$52.35$$

Solution

Question 10

$$20$$ hours

$$31$$ hours

$$25$$ hours

$$27$$ hours

Solution

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