In a retail market,fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying numbers of mangoes. The following was the distribution of mangoes according to the number of boxes.

Number of mangoes	$50$-$52$	$53$-$55$	$56$-$58$	$59$-$61$	$62$-$64$
Number of boxes	$15$	$110$	$135$	$115$	$25$

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

The following data gives the distribution of total monthly household expenditure of $200$ families of a village. Find the modal monthly expenditure of the families. Also,find the mean monthly expenditure:
$\begin{array}{|c|c|} \hline \text{Expenditure (in Rs)} & \text{Number of families} \\ \hline 1000-1500 & 24 \\ 1500-2000 & 40 \\ 2000-2500 & 33 \\ 2500-3000 & 28 \\ 3000-3500 & 30 \\ 3500-4000 & 22 \\ 4000-4500 & 16 \\ 4500-5000 & 7 \\ \hline \end{array}$

$100$ 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.

$A$ class teacher has the following absentee record of $40$ students of a class for the whole term. Find the mean number of $days$ a student was absent.
$\begin{array}{|l|c|c|c|c|c|c|c|} \hline \text{Number of days} & 0-6 & 6-10 & 10-14 & 14-20 & 20-28 & 28-38 & 38-40 \\ \hline \text{Number of students} & 11 & 10 & 7 & 4 & 4 & 3 & 1 \\ \hline \end{array}$

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Runs scored	Number of batsmen
$3000-4000$	$4$
$4000-5000$	$18$
$5000-6000$	$9$
$6000-7000$	$7$
$7000-8000$	$6$
$8000-9000$	$3$
$9000-10000$	$1$
$10000-11000$	$1$

Find the mode of the data.

The following data provides information on the observed lifetimes (in $hours$) of $225$ electrical components:

Lifetimes (in hours)	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$	$100-120$
Frequency	$10$	$35$	$52$	$61$	$38$	$29$

Determine the modal lifetimes of the components.