The table below shows the daily expenditure on food of $25$ households in a locality.

Daily expenditure (in $Rs.$)	$100-150$	$150-200$	$200-250$	$250-300$	$300-350$
Number of households	$4$	$5$	$12$	$2$	$2$

Find the mean daily expenditure on food by a suitable method.

The annual profits earned by $30$ shops of a shopping complex in a locality give rise to the following distribution:

Profit (Rs in lakhs)	Number of shops (frequency)
More than or equal to $5$	$30$
More than or equal to $10$	$28$
More than or equal to $15$	$16$
More than or equal to $20$	$14$
More than or equal to $25$	$10$
More than or equal to $30$	$7$
More than or equal to $35$	$3$

Draw both ogives for the data above. Hence,obtain the median profit.

$A$ survey regarding the heights (in $cm$) of $51$ girls of Class $X$ of a school was conducted and the following data was obtained:

Height (in $cm$)	Number of girls
Less than $140$	$4$
Less than $145$	$11$
Less than $150$	$29$
Less than $155$	$40$
Less than $160$	$46$
Less than $165$	$51$

Find the median height.

The distribution below gives the weights of $30$ students of a class. Find the median weight of the students.

Weight (in kg)	$40-45$	$45-50$	$50-55$	$55-60$	$60-65$	$65-70$	$70-75$
Number of students	$2$	$3$	$8$	$6$	$6$	$3$	$2$

The following table gives the literacy rate (in percentage) of $35$ cities. Find the mean literacy rate.

Literacy rate (in $\%$)	$45-55$	$55-65$	$65-75$	$75-85$	$85-95$
Number of cities	$3$	$10$	$11$	$8$	$3$

$100$ surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

Number of letters	$1-4$	$4-7$	$7-10$	$10-13$	$13-16$	$16-19$
Number of surnames	$6$	$30$	$40$	$16$	$4$	$4$

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also,find the modal size of the surnames.