Presentation of Data Test

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Presentation of Data Test - 27

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following graphs should be used to represent the percentage of boys and girls in a class?

A
Bar graph

B
Pie chart

C
Line graph

D
Venn diagram

Solution

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.
Question 2
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The pie chart shows the examination grades obtained by a group of students. Which of the following statements about the pie chart is true?

A
$$15\, \%$$ of the students scored grade $$B$$

B
$$90\, \%$$ of the students scored grade $$A$$

C
$$\displaystyle \frac{1}{4}$$ of the students scored grade $$B$$

D
$$\displaystyle \frac{1}{3}$$ of the students scored grade $$C$$

Solution

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 $$C$$.
Question 3
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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

A
Hindi

B
Science

C
Social Science

D
English

Solution

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 $$=\displaystyle \frac{55^{\circ}}{360^{\circ}}\times 100=15.28\% $$
Question 4
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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?

A
$$\displaystyle \frac { 800 }{ 17 } %$$

B
$$20\%$$

C
$$35\%$$

D
$$40\%$$

Solution

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 = $$\displaystyle \left( \frac { { 144 }^{ o } }{ { 360 }^{ o } } \times 100 \right) \%=40\%$$
Question 5
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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 numberof handphones sold is 15. Find the number of handphones sold on Thursday.

A
$$6$$

B
$$12$$

C
$$18$$

D
$$24$$

Solution

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 $$ = 6 \times 3 = 18 $$
Question 6
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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:

A
$$700$$

B
$$600$$

C
$$200$$

D
$$500$$
Question 7
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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 8
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The given double graph shows the average heights of boys and girls at specific ages Which conclusion is supported by the graph?

A
Girls are taller than boys until the age of $$14$$

B
Girls and boys grow the same amount each year

C
After the age of $$14$$ boys grow faster than girls

D
Boys are always taller than girls

Solution

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.
Question 9
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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 10
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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. % $$=\displaystyle \frac{90^{\circ}}{360^{\circ}}\times 100=25\% $$