The mean of $15$ observations is $25$. Later on,it was found that one observation was taken by mistake as $20$ instead of $50$. Then,the correct mean is:

In the following distribution:

Monthly income range (in $Rs.$)	Number of families
Income more than $10000$	$100$
Income more than $13000$	$85$
Income more than $16000$	$69$
Income more than $19000$	$50$
Income more than $22000$	$33$
Income more than $25000$	$15$

The number of families having an income range (in $Rs.$) of $16000-19000$ is:

Is it true to say that the mean,mode,and median of grouped data will always be different? Justify your answer.

In a maths test taken by $35$ students,the average score of $15$ girls is $10$ and that of $20$ boys is also $10$. Which of the following can be calculated based on the data we have?

Find the median of the following frequency distribution:

Class	$5-10$	$10-15$	$15-20$	$20-25$	$25-30$	$30-35$	$35-40$	$40-45$
Frequency	$5$	$6$	$15$	$10$	$5$	$4$	$2$	$2$

The median of the following frequency distribution is $50$ and the total frequency is $60$. Find the missing frequencies $x$ and $y$.

Class	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$
Frequency	$5$	$x$	$20$	$y$	$2$