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CBSE Questions for Class 11 Commerce Economics Presentation Of Data Quiz 7 - MCQExams.com
CBSE
Class 11 Commerce Economics
Presentation Of Data
Quiz 7
Find the sales of salesman $$B$$.
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0%
Rs. $$10,000$$
0%
Rs. $$12,000$$
0%
Rs. $$18,000$$
0%
None of these
Explanation
$$
The\quad circle\quad in\quad a\quad pie\quad chart\quad represents\quad { 360 }^{ o }.\\ When\quad Central\quad angle\quad for\quad Salesman\quad A\quad is\quad { 90 }^{ o }\quad \rightarrow \quad Total\quad sales\quad done\quad by\quad Salesman\quad A\quad in\quad 1\quad week\quad is\quad Rs.18000\\ For\quad total\quad angle\quad { 360 }^{ o },\quad totol\quad sale\quad by\quad all\quad =\quad \dfrac { 18000 }{ 90 } \quad \times \quad { 360 }\quad =\quad Rs.\quad 72000\\ Sale\quad by\quad salesman\quad B\quad =\quad \dfrac { 120 }{ 360 } \quad \times \quad 72000\quad =\quad Rs.\quad 24000\\ Sale\quad by\quad salesman\quad C\quad =\quad \dfrac { 80 }{ 360 } \quad \times \quad 72000\quad =\quad Rs.\quad 16000\\ Sale\quad by\quad salesman\quad D\quad =\quad \dfrac { 70 }{ 360 } \quad \times \quad 72000\quad =\quad Rs.\quad 14000
$$
How many watches were sold in all 5 months?
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0%
160
0%
180
0%
175
0%
170
Explanation
Total Sales= Addition of sales individually in each month.
Total Sale$$=20+50+20+60+30=180$$
If the dairy sector receives Rs. $$20$$ crores, then find the total loan disbursed.
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0%
$$120$$ crore Rs.
0%
$$140$$ crore Rs.
0%
$$160$$ crore Rs.
0%
$$180$$ crore Rs.
Explanation
Suppose total loan $$= x$$
Part of dairy will be $$= x\times \left (\dfrac {40}{360}\right)$$
$$\Rightarrow x\times \left (\dfrac {40}{360}\right) = 20$$
$$\Rightarrow x = 20\times \left (\dfrac {360}{40}\right)$$
$$\Rightarrow x = 180$$
So, total loan is $$180$$ crore Rs.
The salesman with the highest sale is:
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0%
$$A$$
0%
$$B$$
0%
$$C$$
0%
$$D$$
Explanation
In a given pie chart, Salesman B has the greatest angle i.e. $$120°$$ when compared to other salesmen.
Also, we know that in a circle, greater the angle of an arc, greater the area.
$$ \therefore $$ Salesman B has the highest sale.
Refer the pie chart and answer.
To show the distribution of proteins and other dry elements in the human body, the arc of the circle should subtend at the center an angle of:
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0%
$$120^o$$
0%
$$54^o$$
0%
$$108^o$$
0%
$$252^o$$
Explanation
Percentage of proteins and other dry elements in the body is ($$16\% + 14\%) $$ which is equal to $$ 30\%$$
$$\therefore$$ Central angle corresponding to proteins and other dry elements together $$=30\% \ of \ 360^\circ$$
$$\Rightarrow \dfrac{30}{100} \times 360$$
$$=108^\circ$$
Find the difference between the highest sale and the lowest sale.
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0%
8000
0%
10000
0%
6000
0%
5000
Explanation
Given:- Sale due to salesman A = 18000
Here, Sale due to A = $$ \cfrac{\text{area of circle}}{4} = 18000$$
Let the radius be r.
$$ \Rightarrow \cfrac{\pi r^2}{4} = 18000 $$
$$ \Rightarrow r^2 = \cfrac{18000.4}{\pi} $$
Sales due to A is area formed by A
Area of arc = $$ \cfrac{\theta \times r^2}{2} $$
Also, we know that arc with maximum or greatest angle with serve the greatest area.
$$ \Rightarrow $$ greatest area = highest sale
Also, arc with smallest angle will serve the smallest area
$$ \Rightarrow $$ Smallest area = Lowest sale
$$ \therefore $$ Highest sale will be due to Salesman B
and Lowest sale will be due to Salesman D
Sale due to B = Area covered by B
$$ = \cfrac{\cfrac{2\pi}{3} \times r^2}{2} $$
$$ = \cfrac{2\pi}{3 \times 2} \times \cfrac{18000 \times 4}{\pi} $$
=$$ 24000$$ Rs
Sale due to D = Area covered by D
$$ = \cfrac{\cfrac{7\pi}{9} \times r^2}{2} $$
$$ = \cfrac{7\pi}{9 \times 2} \times \cfrac{18000 \times 4}{\pi} $$
= $$14000$$ Rs
Difference = Highest Sale - Lowest Sale
= Sale due to B - Sale due to D = $$24000 - 14000 = 10000$$
By how many votes did the winner defeat the nearest contestant?
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0%
20
0%
40
0%
60
0%
100
Explanation
Total number of votes $$= 720$$
Nashima was the winner with central angle as $${ 120 }^{ o }$$.
The next person to get maximum votes was Albert with central angle as $${ 100 }^{ o }$$.
Difference between their angles $$= 120 -100= { 20 }^{ o }$$
So, the number of votes by which Nashima defeated Albert $$ = \dfrac { 20 }{ 360 }\times 720= 40$$ votes.
In statistics a suitable graph for representing the partitioning of total into sub parts is?
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0%
A bar graph
0%
A picto graph
0%
A pie graph
0%
A line graph
Explanation
In statistics a suitable graph for representing the partitioning of total into sub parts is a pie graph.
The adjoining diagram illustrates the information collected about the number of brothers of the boys in a certain group.
What is the total number of boys in this group ?
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0%
$$22$$
0%
$$5$$
0%
$$21$$
0%
$$16$$
Explanation
Total number of boys $$ = 2 + 5 + 4+7 +3+1 = 22 $$
Find the total sale
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0%
72000
0%
36000
0%
24000
0%
14000
Explanation
The circle in a pie chart represents $${ 360 }^{ o }$$.
When Central angle for Salesman $$A$$ is $${ 90 }^{ o } $$
Total sales done by Salesman $$A$$ in $$1$$ week is Rs. $$18000$$
For total angle $${ 360 }^{ o }$$, total sales by all $$=\dfrac { 18000 }{ 90 } \times { 360 }=$$ Rs. $$72000
$$
Nashima had ______ the election.
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0%
won
0%
lose
0%
Can't be determined
0%
None of these
Explanation
In the given piechart, we know that Nashima had created the greatest arc in the circle.
As we know that the arc with the greatest angle covers the greatest area.
Here, the greatest angle is 120°, which is of for Nashima's vote.
Thus, Nashima gets the maximum vote.
$$ \therefore $$ Nashima won the election.
Which of the following graphs should be used to represent the percentage of boys and girls in a class?
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0%
Bar graph
0%
Pie chart
0%
Line graph
0%
Venn diagram
Explanation
Pie chart.
It is
a type of graph in which a circle is divided into sectors such that each represents a proportion of the whole.
Percentage is usually represented with the help of these sectors.
The pie chart shows the examination grades obtained by a group of students. Which of the following statements about the pie chart is true?
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0%
$$15\, \%$$ of the students scored grade $$B$$
0%
$$90\, \%$$ of the students scored grade $$A$$
0%
$$\displaystyle \frac{1}{4}$$ of the students scored grade $$B$$
0%
$$\displaystyle \frac{1}{3}$$ of the students scored grade $$C$$
Explanation
Since the total angle at the centre of a circle is $$ {360}^{o} $$ angle for $$C$$ is $$ {360}^{o} - {90}^{o} - {150}^{o} = {120}^{o} $$
Since $$ {120}^{o} = \dfrac {1}{3} \times {360}^{o} $$, the correct answer is $$ \dfrac {1}{3} $$ of the students scored grade $$C$$.
The given pie chart shoes the marks scored by a student in five different subjects English Hindi Mathematics Science and Social Science Assuming that the total marks obtained for the examination are $$540$$ Find the subject in which the student scored $$22.2\%$$ marks
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0%
Hindi
0%
Science
0%
Social Science
0%
English
Explanation
Calculating the percentage of marks in different subjects we get
Hindi $$=\displaystyle \frac{70^{\circ}}{360^{\circ}}\times 100=19.4\% $$
Science $$=\displaystyle \frac{80^{\circ}}{360^{\circ}}\times 100=22.2\% $$
Social Science $$=\displaystyle \frac{65^{\circ}}{360^{\circ}}\times 100=18.1\% $$
English $$=\displaystyle \frac{55^{\circ}}{360^{\circ}}\times 100=15.28\% $$
If XYZ Auto Company sold 23,000 vehicles in 1999, how many were SUV's?
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0%
2,990
0%
3,030
0%
3,450
0%
4,760
0%
4,775
The bar chart shows the number of handphones sold by a shop in 5 days of a certain week. The difference between the highest number and the lowest number
of handphones sold isFind the number of handphones sold on Thursday.
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0%
$$6$$
0%
$$12$$
0%
$$18$$
0%
$$24$$
Explanation
Highest number of phones were sold on Friday and lowest number were sold on Wednesday.
The difference in their heights is $$ 5 $$ unit squares which is found by counting the difference in the height of their bars.
But the given difference is $$ 15 $$
$$ => 5 units = 15 $$
$$1\ unit = 3\ phones $$
On counting, the bar drawn for Tuesday occupies $$ 6 $$ units.
So, number of phones sold on Tuesday $$ = 6 \times 3 = 18 $$
The pie chart given below shows the expenses incurred and saving by a family in a month. What is the percentage of expenses incurred on account of recreation?
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0%
$$\displaystyle \frac { 800 }{ 17 } %$$
0%
$$20\%$$
0%
$$35\%$$
0%
$$40\%$$
Explanation
Sector angle corresponding to recreation
$$\displaystyle ={ 360 }^{ o }-\left( { 72 }^{ o }+{ 90 }^{ o }+{ 54 }^{ o } \right) $$
$$\displaystyle ={ 360 }^{ o }-{ 216 }^{ o }$$
$$\displaystyle ={ 144 }^{ o }$$
$$\displaystyle \therefore $$ $$\%$$ age expenses incurred on account of recreation = $$\displaystyle \left( \frac { { 144 }^{ o } }{ { 360 }^{ o } } \times 100 \right) \%=40\%$$
The table shows the number of three different brands of laptops sold by a certainstore. The data are respresented by the pie chart which shows a semicircledivided into six equal sectors. The angle of sector representing the number
of Bell laptops sold is:
Brand
Number of laptops
Ace
60
Bell
40
Compact
20
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0%
$$\angle PQR$$
0%
$$\angle ROV$$
0%
$$\angle QOT$$
0%
$$\angle POU$$
Explanation
Answer:-
Let circle represents total no. of laptops = 60 + 40 + + 20 = 120
Area of semicircle = $$ \cfrac{120}{2} $$ = 60
For PSV since they are divided into equal parts
Area of each part = $$ \cfrac{60}{6} = 10 $$
Now No. o laptops of Bell = 40
$$\therefore$$ combination of any four continuous parts from six gives the no. of laptops of Bell.
$$ \Rightarrow \angle { ROV }=\angle { ROS }+\angle { SOT }+\angle { TOU }+\angle { UOV } $$
$$ \angle{ROV} = 10 + 10 + 10 + 10 = 40 $$
A school has strength of $$2000$$ students. The following pie graph shows the interests
of students in different subjects. The number of students interested in Maths is:
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0%
$$700$$
0%
$$600$$
0%
$$200$$
0%
$$500$$
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?
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0%
Rs 450
0%
Rs 625
0%
Rs 675
0%
Cannot be computed from the given data.
Explanation
Using the formula for area of a sector, monthly expenditure on transport
=$$\displaystyle \frac { { 15 }^{ o } }{ { 360 }^{ o } } \times Rs.15000=Rs.625$$.
The given double graph shows the average heights of boys and girls at specific ages Which conclusion is supported by the graph?
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0%
Girls are taller than boys until the age of $$14$$
0%
Girls and boys grow the same amount each year
0%
After the age of $$14$$ boys grow faster than girls
0%
Boys are always taller than girls
Explanation
Till age $$10$$, boys and girls grow the same. From $$10$$ to $$12$$, girls grow faster.
And after the age of $$14$$ boys grow faster than girls.
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?
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0%
$$\displaystyle 116^{\circ}$$
0%
$$\displaystyle 128^{\circ}$$
0%
$$\displaystyle 192^{\circ}$$
0%
$$\displaystyle 212^{\circ}$$
Explanation
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 $$=\dfrac{96}{270}\times 360=128^{\circ}$$
From the pie graph shown alongside Find the percent of students that are seventh grades
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0%
$$35\%$$
0%
$$40\%$$
0%
$$25\%$$
0%
$$28\%$$
Explanation
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. % $$=\displaystyle \frac{90^{\circ}}{360^{\circ}}\times 100=25\% $$
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?
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0%
Rs. $$20800$$
0%
Rs. $$17600$$
0%
Rs. $$21600$$
0%
Rs. $$20000$$
Explanation
Profit made in February $$=27\%$$ of $$80000$$
$$\dfrac{27}{100}\times 80000=$$ Rs. $$21600$$
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?
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0%
$$60$$
0%
$$65$$
0%
$$80$$
0%
$$110$$
Explanation
Angle represent the wheat=$$\dfrac{55000}{180000}\times 360=110^{\circ}$$
Let m be the mid-point be the upper class limit of a continuous frequency distribution The lower class limit of the class is
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0%
$$2m+L$$
0%
$$2m-L$$
0%
$$m-L$$
0%
$$m+2L$$
Explanation
$${\textbf{Step -1: Explain tabulation of a data.}}$$
$${\text{Let a be lower class limit, 1 is the upper class limit and m is the midpoint.}}$$
$${\text{then, midpoint m}}$$
$$ = \dfrac{{a + L}}{2}$$
$$\therefore$$ $$a=2m-L$$
$${\textbf{Hence , option B is correct.}}$$ $$\mathbf{(a=2m-L)}$$
If 7,650 trucks were sold in 1999, how many total vehicles were sold in 1999 by XYZ Auto Company?
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0%
35,000
0%
40,000
0%
45,000
0%
50,000
0%
55,000
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)
Report Question
0%
$$165$$
0%
$$140$$
0%
$$130$$
0%
$$110$$
Explanation
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
$$\displaystyle =15+25+20+20+15+20+25$$
$$\displaystyle =140$$
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.
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0%
Yes
0%
No
0%
Data insufficient
0%
None
Explanation
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 $$\angle DOA$$.
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
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0%
250 crore
0%
150 crore
0%
300 crore
0%
200 crore
Explanation
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=$$\dfrac{72^{\circ}}{360^{\circ}}\times 1000=200 crore.$$
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