Question

the table given below show the number of valid votes obtained by five students competing for the post of a house captain of a school . complete the given table and draw a pie chart .

Answer 1

${\large{\bold{\sf{\underline{GIVEN \; QUESTION:-}}}}}$

the table given below show the number of valid votes obtained by five students competing for the post of a house captain of a school . complete the given table and draw a pie chart

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{cccc}\sf name \: of \: the \: candidate &\sf no. \: of \: valid \: votes&\sf measure \: of \: central \: angle \\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf vikas&\sf 50 &\sf \emptyset_1 \\\\\sf vijay &\sf x &\sf 50 \degree \\\\\sf ajay&\sf 10&\sf \emptyset_2 \\\\\sf vikram&\sf y&\sf 40 \degree\\\\\sf gaurav&\sf 75 &\sf \emptyset_3 \\\\\sf \\\ \sf Total &\sf180 &\sf 360 \degree\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{\bf{}}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}$

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${\large{\bold{\sf{\underline{REQUIRED \; ANSWER:-}}}}}$

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We know that , the total number of valid votes = 180

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★ measure of Central angle of the sector representing a component

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${\bold{\sf{:\implies ( \dfrac{value \: of \: the \: component}{total \: value} \times 360 \degree) }}}$

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${\bold{\sf{:\implies \therefore \emptyset_1 = ( \dfrac{ 50 }{180} \times 360 \degree) = 100 \degree }}}$

${\bold{\sf{:\implies \therefore \emptyset_1 = ( \dfrac{ 10 }{180} \times 360 \degree) = 20 \degree }}}$

and

${\bold{\sf{:\implies \therefore \emptyset_1 = ( \dfrac{ 75 }{180} \times 360 \degree) = 150 \degree }}}$

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★ value of a component

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${\bold{\sf{:\implies ( \dfrac{measure\: of \: the \: central \: angle}{360 \degree} \times total \: value) }}}$

${\bold{\sf{:\implies \therefore x = ( \dfrac{ 50 \degree }{360 \degree} \times180 ) = 25}}}$

and

${\bold{\sf{:\implies \therefore x = ( \dfrac{ 50 \degree }{360 \degree} \times180 ) = 20}}}$

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hence the completed table is as follow :-

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$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{cccc}\sf name \: of \: the \: candidate &\sf no. \: of \: valid \: votes&\sf measure \: of \: central \: angle \\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf vikas&\sf 50 &\sf 100 \degree \\\\\sf vijay &\sf 25 &\sf 50 \degree \\\\\sf ajay&\sf 10&\sf 20 \degree \\\\\sf vikram&\sf 20&\sf 40 \degree\\\\\sf gaurav&\sf 75 &\sf 150 \degree\\\\\sf \\\ \sf Total &\sf180 &\sf 360 \degree\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{\bf{}}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}$

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Now we draw the pie chart using the following steps of construction:

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1. Draw a circle of any convenient radius.

2. Using the protractor, draw sectors corresponding to the central angles calculated in the table above.

3. write the names and measure of Central angle in the sectors so obtained differently.

4. Label each sector. Thus, we obtain the required pie chart as shown in Attachment

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${\large{\bold{\sf{\underline{KNOW \; MORE :-}}}}}$

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PIE CHART -

• A pie chart is a circular diagram in which the components (observations) are represented by the non-intersecting sectors of a circle.

• The size of each sector is proportional to the magnitude of the component (observation) it represents and the whole circle depicts the sum of the values of the components.

• So, each sector shows a fraction of the total. Pie charts are also called circle graphs.

CENTRAL ANGLE FOR A COMPONENT -

• The sectors of a pie chart are constructed in such a way that their areas are directly proportional to the values of the corresponding components.

• We also know that the area of a sector is proportional to the angle made by the arc at the centre.

• Thus, we conclude that the central angle of each sector is proportional to the corresponding value of the component.

• Since the sum of all the central angles of a circle is 360°, we have

${\bold{\sf{:\implies \: central \: angle \: of \: a \: component \: = \: ( \dfrac{value \: of \: the \: component}{total \: value} \times 360 \degree) }}}$

Answer 2

Answer:

the table given below show the number of valid votes obtained by five students competing for the post of a house captain of a school . complete the given table and draw a pie chart .