Represent the following data by means of a histogram:
Class $0-5$ $5-10$ $10-20$ $20-30$ $30-50$ $50-70$
Frequency $5$ $7$ $12$ $16$ $24$ $16$

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Here,the class intervals have unequal widths. Therefore,we must first compute the adjusted frequencies for each class. The minimum class size is $5 - 0 = 5$. The adjusted frequencies are calculated using the following formula:
$\text{Adjusted frequency of a class} = \frac{\text{Frequency of the class}}{\text{Class size}} \times \text{Minimum class size}$
The adjusted frequencies are calculated in the table below:
Class Frequency Class size Adjusted frequency (Height of rectangle)
$0-5$ $5$ $5$ $(5/5) \times 5 = 5$
$5-10$ $7$ $5$ $(7/5) \times 5 = 7$
$10-20$ $12$ $10$ $(12/10) \times 5 = 6$
$20-30$ $16$ $10$ $(16/10) \times 5 = 8$
$30-50$ $24$ $20$ $(24/20) \times 5 = 6$
$50-70$ $16$ $20$ $(16/20) \times 5 = 4$

Using these adjusted frequencies,we plot the histogram where the $x$-axis represents the class intervals and the $y$-axis represents the adjusted frequencies (heights of the rectangles).

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