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 mean of the data: $2, 8, 6, 5, 4, 5, 6, 3, 6, 4, 9, 1, 5, 6, 5$ is given to be $5$. Based on this information,is it correct to say that the mean of the data: $10, 12, 10, 2, 18, 8, 12, 6, 12, 10, 8, 10, 12, 16, 4$ is $10$? Give reason.

Following is the frequency distribution of total marks obtained by the students of different sections of Class $VIII.$
Marks $100-150$ $150-200$ $200-300$ $300-500$ $500-800$
Number of students $60$ $100$ $100$ $80$ $180$
Draw a histogram for the distribution above.

The marks obtained (out of $100$ marks) by $50$ students in a mathematics test are as given below:
$\begin{array}{lrrrrrrrrr} 10, & 65, & 75, & 37, & 8, & 58, & 35, & 42, & 29, & 52 \\ 19, & 52, & 23, & 61, & 88, & 65, & 18, & 77, & 85, & 49, \\ 12, & 7, & 41, & 75, & 52, & 90, & 30, & 89, & 95, & 62, \\ 16, & 61, & 35, & 68, & 22, & 72, & 56, & 27, & 62, & 93, \\ 25, & 59, & 48, & 81, & 26, & 84, & 60, & 39, & 76, & 50 \end{array}$
Represent the data given above by a grouped frequency distribution table,taking the class intervals as $0-10, 10-20, \dots$ etc.

Heights (in $cm$) of $30$ girls of Class $IX$ are given below:
$140, 140, 160, 139, 153, 153, 146, 150, 148, 150, 152$
$146, 154, 150, 160, 148, 150, 148, 140, 148, 153, 138$
$152, 150, 148, 138, 152, 140, 146, 148$
Prepare a frequency distribution table for this data.

Give five examples of secondary data that you can collect from your day-to-day life.

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