Presentation of Data Test

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Presentation of Data Test - 28

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Weekly Quiz Competition

Question 1
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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 2
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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 3
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Let m be the mid-point be the upper class limit of a continuous frequency distribution The lower class limit of the class is

A
$$2m+L$$

B
$$2m-L$$

C
$$m-L$$

D
$$m+2L$$

Solution

$${\textbf{Step -1: Explain tabulation of a data.}}$$
$${\text{Let a be lower class limit, 1 is the upper class limit and m is the midpoint.}}$$
$${\text{then, midpoint m}}$$ $$ = \dfrac{{a + L}}{2}$$
$$\therefore$$ $$a=2m-L$$
$${\textbf{Hence , option B is correct.}}$$ $$\mathbf{(a=2m-L)}$$
Question 4
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The diagram shows the histogram of the amount of time spent watching TV in a day for a group of students. Remember that the area of each rectangle is proportional to its frequency. Find the total number of students. (Take the most common base of all rectangles as 1 unit)

A
$$165$$

B
$$140$$

C
$$130$$

D
$$110$$

Solution

The most common base is $$50$$, so it is taken as $$1$$ unit.
For the class $$100 - 200$$, the base is $$2$$ units.
For the class $$200 - 225$$ and $$225 - 250$$, the base $$\displaystyle =\frac { 1 }{ 2 } $$unit
$$\displaystyle \therefore $$ For the class $$100 - 200$$,
The actual frequency $$=$$ $$\displaystyle 10\times 2=20$$
For the class $$200 - 225$$,
The actual frequency $$=$$ $$\displaystyle 40\times \frac { 1 }{ 2 } =20$$
For the class $$225 - 250$$,
the actual frequency $$=$$ $$\displaystyle 30\times \frac { 1 }{ 2 } =15$$
$$\displaystyle \therefore $$ Total number of students
$$\displaystyle =15+25+20+20+15+20+25$$
$$\displaystyle =140$$
Question 5
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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 6
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Allocations to various sectors of the yearly budget for Rs. 1000 crore are represented by the following pie diagram. The expenditure (in rupees) on agriculture is

A
250 crore

B
150 crore

C
300 crore

D
200 crore

Solution

A full circle has $$360^{\circ}$$
$$\therefore $$angle of agriculture=$$360^{\circ}-(18^{\circ}+90^{\circ}+72^{\circ}+54^{\circ}+54^{\circ})$$
$$\Rightarrow 360^{\circ}-288^{\circ}=72^{\circ}$$
yearly budget=Rs.1000 crore
$$\therefore $$Expenditure on agriculture=$$\dfrac{72^{\circ}}{360^{\circ}}\times 1000=200 crore.$$
Question 7
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Two houses A and B were constructed at a total cost of Rs 100000 and Rs 250000 respectively The expenditure on materials is shown in the pie charts given bellow
The expenditure on B exceeds expenditure on A by :

A
Rs $$12500$$

B
Rs $$15000$$

C
Rs $$10000$$

D
Rs $$22000$$

Solution

Answer:-
Shaded area = Materials
Given:- Area of circle A = Total cost of construction of A = Rs $$100000$$
$$\pi {r_1}^2 = 100000$$
$$\Rightarrow \;{r_1}^2=\cfrac{100000}{\pi}$$
Now expenditure on material for A = Area covered by material in circle A = $$\cfrac{\pi {r_1}^2}{2}$$
$$E_A = \cfrac{\pi \times 100000}{2\times \pi}=50000$$
Similarly: Area of B = Total cost of construction of A = Rs $$250000$$
$$\pi {r_2}^2 = 250000$$
$${r_2}^2 = \cfrac{250000}{\pi}$$
Now expenditure on material for B = Area covered by material in circle B = $$\cfrac{\pi {r_1}^2}{4}$$
$$E_B = \cfrac{\pi \times 250000}{4\times \pi}=62500$$
Answer: expenditure on material for B - expenditure on material for A = $$62500 - 50000 = 12500$$
Question 8
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The following table gives information regarding land holdings of household of a village
Size of land holding Number of houehold
More than 1 acre 1727
More than 2 acre 1268
More than 3 acre 378
More than 4 acre 155
More than 5 acre 52
in the village there are 2270 households. The number of households having land up to 1 acre is

A
1727

B
459

C
543

D
378

Solution

Total no. of households in the village $$=2270$$
Total no. of households in the village who has land more than one acre $$=1727$$

Hence,
Total no. of households having land up to one acre $$=2270-1727\Rightarrow 543.$$
Question 9
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Study the above graph and calculate the difference between the number of cars manufactured by company $$Y$$ in $$2001$$ and $$2000$$?

A
$$20000$$

B
$$30000$$

C
$$40000$$

D
$$50000$$

Solution

Number of cars manufactured by company $$Y$$ in $$2001$$ $$=80000$$
Number of cars manufactured by company $$Y$$ in $$2000$$ $$= 100000$$
The difference is $$ 100000-80000 = 20000$$
Question 10
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Directions For Questions

900 men volunteered for joining the armed force. study the pie-graph and answer the following

...view full instructions

How many men volunteered for navy and marine?

A
150, 125

B
125, 375

C
250, 150

D
125, 150

Solution

No of men joining navy force $$=\dfrac{60}{360}\times 900=150$$
No of men joining marine force $$=\dfrac{80}{360}\times 900=125$$