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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Similar Questions

For the following data,draw a frequency polygon:
Class $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$
Frequency $1$ $4$ $5$ $10$ $5$ $4$ $1$

Draw a histogram to represent the following grouped frequency distribution:
Ages (in years) Number of teachers
$20-24$ $10$
$25-29$ $28$
$30-34$ $32$
$35-39$ $48$
$40-44$ $50$
$45-49$ $35$
$50-54$ $12$

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

The marks obtained (out of $25$ marks) by $40$ students in an examination are as given below:
$\begin{array}{rrrrrrrrrr} 8, & 12, & 23, & 9, & 5, & 20, & 16, & 3, & 6, & 23 \\ 10, & 6, & 21, & 1, & 18, & 17, & 18, & 16, & 16, & 12, \\ 3, & 15, & 21, & 7, & 12, & 5, & 2, & 7, & 13, & 24, \\ 13, & 18, & 8, & 2, & 20, & 5, & 13, & 7, & 23, & 16 \end{array}$
Represent the data given above by a grouped frequency distribution table,taking the class intervals as $0-5, 5-10, \dots$ etc.

For drawing a frequency polygon of a continuous frequency distribution,we plot the points whose ordinates are the frequencies of the respective classes and abscissae are respectively:

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