For the following data,draw a frequency polygon:
Class $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$
Frequency $1$ $4$ $5$ $10$ $5$ $4$ $1$

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(N/A) To draw a frequency polygon,we first calculate the class marks (mid-values) for each class interval.
Class Mid-value Frequency
$10-20$ $15$ $1$
$20-30$ $25$ $4$
$30-40$ $35$ $5$
$40-50$ $45$ $10$
$50-60$ $55$ $5$
$60-70$ $65$ $4$
$70-80$ $75$ $1$

To close the polygon,we include two imaginary classes: $0-10$ with mid-value $5$ and frequency $0$,and $80-90$ with mid-value $85$ and frequency $0$. Plot these points $(5, 0), (15, 1), (25, 4), (35, 5), (45, 10), (55, 5), (65, 4), (75, 1), (85, 0)$ on a graph and join them with line segments.

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Expenditure on education of a country during a five-year period $(2002-2006)$,in crores of rupees,is given below:
Elementary education$240$
Secondary education$120$
University education$190$
Teacher's training$20$
Social education$10$
Other educational programmes$115$
Cultural programmes$25$
Technical education$125$

Represent the information above by a bar graph.

The mean of $10$ observations is $52$. If $12$ is subtracted from each observation,then the mean of the new observations so obtained is:

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$4$ $4$
$8$ $6$
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If the mean of $20$ observations is $27.2$,then $\Sigma f_{i} x_{i}$ is ............

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