Presentation of Data Test

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Presentation of Data Test - 24

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Question 1
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Directions For Questions

For an experiment in Botany, two different plants, plant A and plant B were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph.

...view full instructions

Were the two plants of the same height during any week shown here? Specify.

A
At the end of the 3rd week

B
At the end of the 1st week

C
At the end of the 2nd week

D
At the end of the 4th week

Solution

In the given graph dotted line represents the growth of plant A and solid line represents the growth of plant B.
From the graph, we can see that the two lines inersect at the end of the second week which means at that point both the plants have the same height (7 cm).
Question 2
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Directions For Questions

A courier person cycles from a town to a neighboring suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph.

...view full instructions

How far is the place of the merchant from the town?

A
$$16$$

B
$$18$$

C
$$20$$

D
$$22$$

Solution

It is given that the courier person travels from town to a neighboring suburban area.

From the graph, we can observe that the destination place is $$22\space k.m.$$ from the town.
Question 3
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Directions For Questions

The following pie diagram represents expenditure on different items in constructing a building. Answer the following questions.

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Find the expenditure on the labours if the total construction cost is Rs. $$5,40,000$$

A
$$1,12,500$$

B
$$1,22,500$$

C
$$1,35,500$$

D
$$1,50,000$$

Solution

Sum of all angles is $$360$$ degrees
Labour $$=100$$ degree
So, part of labour in total construction $$= \dfrac {100}{360}$$
Total construction $$= 5,40,000$$
Labour expenditure $$= 5,40,000\times \left (\dfrac {100}{360}\right)$$
$$= 1,50,000$$
Question 4
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A family spends Rs. $$6,000$$ p.m. to meet the monthly expenditure. The expenditure has been shown in the given pie diagram. The miscellaneous expenditure is

A
Rs. $$1,500$$

B
Rs. $$2,000$$

C
Rs. $$1,200$$

D
Rs. $$3,000$$

Solution

Angle made by rent expenditure $$=$$ angle made by education expenditure $$=60^0$$ ...(vertically opposite angles)
Angle made by miscellaneous expenditure $$=360 - 90 - 30 - 60 - 60 = 120\,^{\circ}$$
Miscellaneous expenditure $$= \dfrac{120 \times 6000}{360} =$$ Rs. $$2000$$
Question 5
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The given component bar diagram shows percentage of marks obtained by a student in different subjects in a test : The height of the line AB from x-axis is

A
21 cm approximately

B
38 cm

C
86 cm approximately

D
48 cm

Solution

In the given diagram. $$AB$$ line is above the physics and mathematics.
From the graph, physics is $$25\%$$ and mathematics is $$32\%$$.
Therefore, line $$AB$$ is $$25+32=57\%$$ away from X-axis.
Given that scale is $$3\%=2$$ cm.
$$ \implies 57\%=\dfrac{57\times2}{3}=\dfrac{114}{3}=38$$ cm
Question 6
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The given histogram shows a frequency distribution of marks obtained by $$56$$ students in a subject.
Number of students securing marks between $$70$$ and $$100$$ is

A
2

B
4

C
6

D
8

Solution

Frequency density
$$ = \dfrac{\text {Frequency in the class}}{\text {Lenght of the class interval}}$$

$$\therefore 0.2 = \dfrac{\text {Frequency in the class}}{100 - 70}$$
Frequency in the class $$= 0.2 \times 30 = 6$$
Question 7
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Directions For Questions

A professor keeps data on students tabulated by performance and sex of the student. The data is kept on a computer disk, but unfortunately some of it is lost because of a virus. Only the following could be recovered.
Performance Total
Average Good Excellent
Male 10
Female 32
Total 30
Picnic buttons were pressed but to no avail. An expert committee was formed, which decided that the following facts were self-evident : Half the students were either excellent of good. 40% of the students were females. One third of the male students were average.
Female students $$=$$ 32 which is 40% of total students. Hence
total number of students $$=\displaystyle \frac{32}{0.4}=80$$
Hence males $$=$$ (80-32)$$=$$48. It is further given, that half the students were either excellent or good and one third of the male students were average. Hence the table can be completed as under :
Performance Total
Average Good Excellent
Male 16 22 10 48
Female 24 8 - 32
Total 40 30 10 80

...view full instructions

How many students are both female and excellent ?

A
0

B
8

C
16

D
32

Solution

In given table we can see, there are not there are not any female whose performance is excellent.
$$\therefore$$ The students are both female and excellent is $$0$$
Question 8
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Allocations to various sectors of the yearly budget for Rs. $$1000$$ crane are represented by the following pie diagram. The expenditure (in rupees) on agriculture is

A
$$250$$ crane

B
$$150$$$ crane

C
$$300$$ crane

D
$$200$$ crane

Solution

Total angle $$= 360\,^{\circ}$$
Thus angle that agriculture makes $$= 360 - 18 - 90 - 72 - 54 - 54 = 72\,^{\circ}$$
$$\therefore$$ the expenditure on agriculture $$= \dfrac{72}{360} \times 1000$$ crane $$= 200$$ crane.
Question 9
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The times, in seconds, taken by 150 atheletes to run a 110 hurdle race are tabulated below :
Class
Frequency
13.8-14
2
14-4.2
4
14.2-14.4
5
14.4-14.6
71
14.6-14.8
48
14.8-15
20
The number of atheletes who completed the race in less then 14.6 seconds is :

A
$$11$$

B
$$71$$

C
$$82$$

D
$$130$$

Solution

The number of athletes who completed the race in $$<14.6$$ seconds is $$n(13.8-14)+n(14-14.2)+n(14.2-14.4)+n(14.4-14.6)$$
$$=2+4+5+71=82$$
Question 10
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Directions For Questions

A courier person cycles from a town to a neighboring suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph.

...view full instructions

When did the person stop on his way?

A
9:00 a.m - 9.30 a.m

B
9:30 a.m - 10.00 a.m

C
10:00 a.m - 10.30 a.m

D
10:30 a.m - 11.00 a.m

Solution

The person had stopped between the time $$10$$ a.m to $$10.30$$ a.m.
This can be easily concluded since the curve on the graph between these times was horizontal to the x-axis which means no distance travelled.
Hence, option C is correct.