Prepare a continuous grouped frequency distribution from the following data:
Mid-point Frequency
$5$ $4$
$15$ $8$
$25$ $13$
$35$ $12$
$45$ $6$

Also,find the size of the class intervals.

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The mid-points are $5, 15, 25, 35,$ and $45.$ The common difference between consecutive class marks is $h = 15 - 5 = 10.$
To find the class intervals,we subtract and add $\frac{h}{2} = \frac{10}{2} = 5$ from each mid-point.
For mid-point $5$: $5 - 5 = 0$ and $5 + 5 = 10$,so the interval is $0-10$.
For mid-point $15$: $15 - 5 = 10$ and $15 + 5 = 20$,so the interval is $10-20$.
For mid-point $25$: $25 - 5 = 20$ and $25 + 5 = 30$,so the interval is $20-30$.
For mid-point $35$: $35 - 5 = 30$ and $35 + 5 = 40$,so the interval is $30-40$.
For mid-point $45$: $45 - 5 = 40$ and $45 + 5 = 50$,so the interval is $40-50$.
The size of the class interval is $10.$
$A$ continuous grouped frequency distribution is given below:
Class Interval Frequency
$0-10$ $4$
$10-20$ $8$
$20-30$ $13$
$30-40$ $12$
$40-50$ $6$

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The following are the marks (out of $100$) of $60$ students in mathematics:
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$45-60$ $30$ $27$
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