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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Similar Questions

The lengths of $62$ leaves of a plant are measured in millimetres and the data is represented in the following table:
Length (in mm) Number of leaves
$118-126$ $8$
$127-135$ $10$
$136-144$ $12$
$145-153$ $17$
$154-162$ $7$
$163-171$ $5$
$172-180$ $3$

Draw a histogram to represent the data above.

Find the mean,the median,and the mode of the observations:
$33, 92, 55, 90, 35, 77, 58, 41, 80, 64, 46$

The class marks of a frequency distribution are given as follows: $15, 20, 25, \ldots$ The class interval corresponding to the class mark $20$ is:

The number of books in different shelves of a library are as follows:
$37, 22, 24, 27, 28, 27, 20, 36, 21, 20,$
$29, 30, 29, 36, 30, 25, 27, 32, 24, 28,$
$34, 20, 25, 28, 30, 20, 35, 25, 27, 31$
Represent the data given above by a grouped frequency distribution table,taking the class intervals as $18-22, 22-26, 26-30, 30-34, 34-38$.

The following table shows a frequency distribution for the speed of cars passing through a particular spot on a highway:
Class interval $(km/h)$ Frequency
$30-40$ $3$
$40-50$ $6$
$50-60$ $25$
$60-70$ $65$
$70-80$ $50$
$80-90$ $28$
$90-100$ $14$

Draw a histogram and a frequency polygon representing the data above.

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