Data Handling Test

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Data Handling Test - 28

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Question 1
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.

A
5

B
60

C
10

D
12

Solution

$$\Rightarrow$$ One symbol represents $$5$$ balloons.
$$\Rightarrow$$ Then, $$60$$ balloons represents how many symbols.
$$\therefore$$ Required symbols $$=\dfrac{60}{5}=12$$
$$\therefore$$ The number of symbols to be drawn to represent $$60$$ ballons is $$12$$
Question 2
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A student represents his scores in Mathematics Statistics and Economics in a pie chart The central angle for Mathematics is $$\displaystyle 120^{\circ}$$ He scored $$96$$ in Statistics and $$84$$ in Economics The central angle for Statistics is?

A
$$\displaystyle 116^{\circ}$$

B
$$\displaystyle 128^{\circ}$$

C
$$\displaystyle 192^{\circ}$$

D
$$\displaystyle 212^{\circ}$$

Solution

Marks in Statistics $$=96$$
Marks in Economics $$=84$$
total angle in a pie chart$$=360^{\circ}$$
Angle for Maths $$=120^{\circ}$$
Angle for Statistics and Economics $$=360-120=240^{\circ}$$
Total marks $$=\dfrac{360}{240}\times (96+84)=270$$
$$\therefore $$ Angle for statics $$=\dfrac{96}{270}\times 360=128^{\circ}$$
Question 3
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From the pie graph shown alongside Find the percent of students that are seventh grades

A
$$35\%$$

B
$$40\%$$

C
$$25\%$$

D
$$28\%$$

Solution

Angle at the centre representing Grade $$7$$
$$=\displaystyle 360^{\circ}-\left ( 126^{\circ}+144^{\circ} \right )=360^{\circ}-270^{\circ}=90^{\circ}$$
$$\displaystyle \therefore $$ Reqd. % $$=\displaystyle \frac{90^{\circ}}{360^{\circ}}\times 100=25\% $$
Question 4
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If one symbol of image(Ref image) Represents $$10$$ bottles of apple juice then $$35$$ bottles of apple juice represented by

A

B

C

D

Solution

$$3$$ full and one half are required to show $$35$$.
Hence the answer is option C
Question 5
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The pie chart shows the profit made by a company in the first $$4$$ months of the year. The total amount of profit made in the $$4$$ months was Rs. $$80000$$. How much profit did the company make in February?

A
Rs. $$20800$$

B
Rs. $$17600$$

C
Rs. $$21600$$

D
Rs. $$20000$$

Solution

Profit made in February $$=27\%$$ of $$80000$$
$$\dfrac{27}{100}\times 80000=$$ Rs. $$21600$$
Question 6
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Which of the following is an outcome?

A
Rolling a pair of dice

B
Landing on red

C
Choosing 2 marbles from a jar

D
None of the above

Solution

An outcome is the result of a single trial of an experiment.
A. Rolling a pair dice is an experiment that results in $$36$$ possible outcomes.
B. Landing on red is an outcome as after performing an experiment, the result can be landing on red.
C. Choosing $$2$$ marbles from a jar cannot be an outcome, because it is not known how many balls are there, but it can be an experiment.
Question 7
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Sapna found the following data in an almanac.

Crop Area planted (in acres)
Wheat $$55,000$$
Corn $$32,500$$
Potatoes $$30,000$$
Lettuce $$40,000$$
Carrots $$22,500$$
Total $$180,000$$

She needs to use it to make a circle graph. What is the best estimate of the number of degrees that should be in the central angle of the section that represents wheat?

A
$$60$$

B
$$65$$

C
$$80$$

D
$$110$$

Solution

Angle represent the wheat=$$\dfrac{55000}{180000}\times 360=110^{\circ}$$
Question 8
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If the monthly expenditure pattern of a person who earns a monthly salary of Rs. 15,000 is represented in a pie graph, then the sector angle of an item on transport expenses measures $$15^o$$. What is his monthly expenditure on transport?

A
Rs 450

B
Rs 625

C
Rs 675

D
Cannot be computed from the given data.

Solution

Using the formula for area of a sector, monthly expenditure on transport
=$$\displaystyle \frac { { 15 }^{ o } }{ { 360 }^{ o } } \times Rs.15000=Rs.625$$.
Question 9
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Out of total of $$1080$$ workers,$$420$$ workers belong to category $$A, 300$$ to category $$B, 225$$ belong to category $$C$$ and $$135$$ are category $$D$$ workers.
Can we represent the given data in a pie chart.

A
Yes

B
No

C
Data insufficient

D
None

Solution

Let us first find out the central angle for the sectors to be represented by these parts.
(i) Category A $$=\dfrac {420}{1080}\times 360^{\circ}=140^{\circ}$$

(ii) Category B $$=\dfrac {300}{1080}\times 360^{\circ}=100^{\circ}$$

(iii) Category C $$=\dfrac {225}{1080}\times 360^{\circ}=75^{\circ}$$

(iv) Category D $$=\dfrac {135}{1080}\times 360^{\circ}=40^{\circ}$$
Let us add the central angles to check their correctness, $$140^{\circ} + 100^{\circ} + 75^{\circ} + 45^{\circ} = 360^{\circ}$$
Draw a circle and mark the radius OA. Then at 0 draw successive angles(in a clockwise direction) of measures $$140^{\circ}, 100^{\circ}, 756^{\circ}$$ and $$45^{\circ}$$, These angles are $$\angle AOB, \angle BOC, \angle COD$$ and $$\angle DOA$$.
Question 10
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The pictogram shows the number of visitors to an exhibition in a particular week. The number of visitors recorded after Wednesday is:

A
$$10$$

B
$$18$$

C
$$60$$

D
$$70$$

Solution

Number of visitors in an exhibition after Wednesday $$=$$ Number of visitors in an exhibition on Thursday + Number of visitors in an exhibition on Friday
Number of visitors in an exhibition after Wednesday $$=$$ $$(6\times 6) + (6\times 4)$$
$$=$$ $$ 36 + 24 = 60$$