Given below is a cumulative frequency distribution showing the marks secured by $50$ students of a class:
Marks Below $20$ Below $40$ Below $60$ Below $80$ Below $100$ Number of students $17$ $22$ $29$ $37$ $50$
Form the frequency distribution table for the data.
| Marks | Below $20$ | Below $40$ | Below $60$ | Below $80$ | Below $100$ |
| Number of students | $17$ | $22$ | $29$ | $37$ | $50$ |
Form the frequency distribution table for the data.
(N/A) To convert the cumulative frequency distribution into a frequency distribution,we subtract the cumulative frequency of the preceding class from the cumulative frequency of the current class.
$1$. For the interval $0-20$,the frequency is $17$.
$2$. For the interval $20-40$,the frequency is $22 - 17 = 5$.
$3$. For the interval $40-60$,the frequency is $29 - 22 = 7$.
$4$. For the interval $60-80$,the frequency is $37 - 29 = 8$.
$5$. For the interval $80-100$,the frequency is $50 - 37 = 13$.
The resulting frequency distribution table is:
$1$. For the interval $0-20$,the frequency is $17$.
$2$. For the interval $20-40$,the frequency is $22 - 17 = 5$.
$3$. For the interval $40-60$,the frequency is $29 - 22 = 7$.
$4$. For the interval $60-80$,the frequency is $37 - 29 = 8$.
$5$. For the interval $80-100$,the frequency is $50 - 37 = 13$.
The resulting frequency distribution table is:
| Marks | Number of students |
| $0-20$ | $17$ |
| $20-40$ | $5$ |
| $40-60$ | $7$ |
| $60-80$ | $8$ |
| $80-100$ | $13$ |
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The mean of the following frequency distribution is $43.75$. Find the missing frequency $f$.
Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$ $90-100$ Frequency $8$ $4$ $20$ $45$ $64$ $32$ $f$ $8$ $2$ $2$
| Class | $0-10$ | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ | $60-70$ | $70-80$ | $80-90$ | $90-100$ |
| Frequency | $8$ | $4$ | $20$ | $45$ | $64$ | $32$ | $f$ | $8$ | $2$ | $2$ |
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| Class | Frequency $(f)$ |
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| $110-120$ | $6$ |
| $120-130$ | $25$ |
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View SolutionThe median of the following frequency distribution is $46$ and the total frequency is $230$. Find the missing frequencies $x$ and $y$.
Class $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ Frequency $12$ $30$ $x$ $65$ $y$ $25$ $18$
| Class | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ | $60-70$ | $70-80$ |
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