The lengths of $40$ leaves of a plant are measured correct to the nearest millimetre,and the data obtained is represented in the following table:

Length (in mm)	Number of leaves
$118-126$	$3$
$127-135$	$5$
$136-144$	$9$
$145-153$	$12$
$154-162$	$5$
$163-171$	$4$
$172-180$	$2$

Find the median length of the leaves.

$A$ life insurance agent found the following data for the distribution of ages of $100$ policy holders. Calculate the median age,if policies are given only to persons having age $18$ years onwards but less than $60$ years.

Age (in years)	Number of policy holders
Below $20$	$2$
Below $25$	$6$
Below $30$	$24$
Below $35$	$45$
Below $40$	$78$
Below $45$	$89$
Below $50$	$92$
Below $55$	$98$
Below $60$	$100$

The following table gives the distribution of the lifetime of $400$ neon lamps:

Life time (in hours)	Number of lamps
$1500-2000$	$14$
$2000-2500$	$56$
$2500-3000$	$60$
$3000-3500$	$86$
$3500-4000$	$74$
$4000-4500$	$62$
$4500-5000$	$48$

Find the median lifetime of a lamp.

The distribution below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets by choosing a suitable method. What does the mean signify?

Number of wickets	$20$-$60$	$60$-$100$	$100$-$150$	$150$-$250$	$250$-$350$	$350$-$450$
Number of bowlers	$7$	$5$	$16$	$12$	$2$	$3$

The following distribution gives the daily income of $50$ workers of a factory.

Daily income (in Rs.)	$100-120$	$120-140$	$140-160$	$160-180$	$180-200$
Number of workers	$12$	$14$	$8$	$6$	$10$

Convert the distribution above to a less than type cumulative frequency distribution,and draw its ogive.

$100$ 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.