The lengths of $40$ leaves of a plant are measured correct to one millimetre,and the obtained data is represented in the following table:
Length (in $mm$) Number of leaves
$118-126$ $3$
$127-135$ $5$
$136-144$ $9$
$145-153$ $12$
$154-162$ $5$
$163-171$ $4$
$172-180$ $2$

$(i)$ Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]
$(ii)$ Is there any other suitable graphical representation for the same data?
$(iii)$ Is it correct to conclude that the maximum number of leaves are $153 \, mm$ long? Why?

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(N/A) $(i)$ It can be observed that the length of leaves is represented in a discontinuous class interval having a difference of $1$ between them.
Therefore,$1/2 = 0.5$ has to be added to each upper class limit and subtracted from each lower class limit to make the class intervals continuous.
Length (in $mm$) Number of leaves
$117.5-126.5$ $3$
$126.5-135.5$ $5$
$135.5-144.5$ $9$
$144.5-153.5$ $12$
$153.5-162.5$ $5$
$162.5-171.5$ $4$
$171.5-180.5$ $2$

Taking the length of leaves on the $x$-axis and the number of leaves on the $y$-axis,the histogram is drawn as shown in the figure.
$(ii)$ Another suitable graphical representation for this data is a frequency polygon.
$(iii)$ No,it is not correct. The maximum number of leaves $(12)$ have their lengths in the range of $144.5 \, mm$ to $153.5 \, mm$. It does not mean that all these leaves are $153 \, mm$ long.

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Consider the marks,out of $100$,obtained by $51$ students of a class in a test,given in the table below. Draw a frequency polygon corresponding to this frequency distribution table.
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$10-20$$10$
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$30-40$$6$
$40-50$$7$
$50-60$$3$
$60-70$$2$
$70-80$$2$
$80-90$$3$
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Total$51$

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$6.$Other causes$22.0$

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