Form the frequency distribution table from the following cumulative frequency data:
Marks (out of $90$) Number of candidates
More than or equal to $80$ $4$
More than or equal to $70$ $6$
More than or equal to $60$ $11$
More than or equal to $50$ $17$
More than or equal to $40$ $23$
More than or equal to $30$ $27$
More than or equal to $20$ $30$
More than or equal to $10$ $32$
More than or equal to $0$ $34$

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(N/A) To form the frequency distribution table,we subtract the cumulative frequencies of consecutive intervals to find the frequency of each specific class interval.
Given that the total number of candidates is $34$ (as seen in the 'More than or equal to $0$' category),we calculate the frequency for each class interval as follows:
Class interval Frequency
$0-10$ $34-32 = 2$
$10-20$ $32-30 = 2$
$20-30$ $30-27 = 3$
$30-40$ $27-23 = 4$
$40-50$ $23-17 = 6$
$50-60$ $17-11 = 6$
$60-70$ $11-6 = 5$
$70-80$ $6-4 = 2$
$80-90$ $4$

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The median class in the following frequency distribution is ..........
Class $20-25$ $25-30$ $30-35$ $35-40$ $40-45$ $45-50$ $50-55$
Frequency $2$ $5$ $8$ $10$ $7$ $10$ $3$

The mode of the following data is $33 \frac{1}{3}$ and the total frequency is $100$. Find the missing frequencies $x$ and $y$.
Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$
Frequency $7$ $12$ $x$ $28$ $y$ $9$

Calculate the mean of the following frequency distribution:
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Frequency $12$ $16$ $8$ $6$ $8$

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Class $50-70$ $70-90$ $90-110$ $110-130$ $130-150$ $150-170$
Frequency $10$ $18$ $7$ $6$ $5$ $4$

Find the mean of the distribution:
Class $1-3$ $3-5$ $5-7$ $7-10$
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