$\displaystyle 250$ apples of a box were weighed and the distribution of masses of the apples is given in the following table :
Mass (in grams) $\displaystyle 80$-$\displaystyle 100$ $\displaystyle 100$-$\displaystyle 120$ $\displaystyle 120$-$\displaystyle 140$ $\displaystyle 140$-$\displaystyle 160$ $\displaystyle 160$-$\displaystyle 180$
Number of apples $\displaystyle 20$ $\displaystyle 60$ $\displaystyle 70$ $\displaystyle x$ $\displaystyle 60$
(i)
Find the value of $\displaystyle x$ and the mean mass of the apples.
(ii)
Find the modal mass of the apples.

Mass	$\displaystyle 80$-$\displaystyle 100$	$\displaystyle 100$-$\displaystyle 120$	$\displaystyle 120$-$\displaystyle 140$	$\displaystyle 140$-$\displaystyle 160$	$\displaystyle 160$-$\displaystyle 180$	Total
No. of apples \(\displaystyle \mathrm{f}_{\mathrm{i}}\)	$\displaystyle 20$	$\displaystyle 60$	$\displaystyle 70$	\(\displaystyle \mathrm{x}=40\)	$\displaystyle 60$	$\displaystyle 250$
\(\displaystyle \mathrm{x}_{\mathrm{i}}\)	$\displaystyle 90$	$\displaystyle 110$	$\displaystyle 130$	$\displaystyle 150$	$\displaystyle 170$
\(\displaystyle \mathrm{x}_{\mathrm{i}} \mathrm{f}_{\mathrm{i}}\)	$\displaystyle 1800$	$\displaystyle 6600$	$\displaystyle 9100$	$\displaystyle 6000$	$\displaystyle 10200$	$\displaystyle 33700$

Marking-scheme solution

Mass (in grams)	$\displaystyle 80$-$\displaystyle 100$	$\displaystyle 100$-$\displaystyle 120$	$\displaystyle 120$-$\displaystyle 140$	$\displaystyle 140$-$\displaystyle 160$	$\displaystyle 160$-$\displaystyle 180$
Number of apples	$\displaystyle 20$	$\displaystyle 60$	$\displaystyle 70$	$\displaystyle x$	$\displaystyle 60$