The densities, $dg/{\mathrm{cm}}^3$, of $125$ chemical compounds are given in the following table.

Density$\left(dg/{\mathrm{cm}}^3\right)$	$d<1.30$	$d<1.38$	$d<1.42$	$d<1.58$	$d<1.70$
No. compounds $\left(cf\right)$	$32$	$77$	$92$	$107$	$125$

Find the frequencies $a, b, c$ and $d$ given in the table below.

Density $\left(dg/{\mathrm{cm}}^3\right)$	$0-$	$1.30-$	$1.38-$	$1.42-1.70$
No. compounds $\left(f\right)$	$a$	$b$	$c$	$d$

The daily journey times for $80$ bank staff to get to work are given in the following table.

How many staff take between $15$ and $45$ minutes to get to work?

The daily journey times for $80$ bank staff to get to work are given in the following table.

Find the exact number of staff who take$\frac{x+y}{2}$ minutes or more to get to work, given that $85\%$ of the staff take less than $x$ minutes and that $70\%$ of the staff take $y$ minutes or more.

A fashion company selected $100$, $12$-year-old boys and $100$, $12$-year-old girls to audition as models. The heights, $h \mathrm{cm}$, of the selected children are represented in the following graph.

What features of the data suggest that the children were not selected at random?

A fashion company selected $100$ $12$-year-old boys and $100$ $12$-year-old girls to audition as models. The heights, $h \mathrm{cm}$, of the selected children are represented in the following graph.

Estimate the number of girls who are taller than the shortest $50$ boys.

A fashion company selected $100$ $12$-year-old boys and $100$ $12$-year-old girls to audition as models. The heights, $h \mathrm{cm}$, of the selected children are represented in the following graph.

What is the significance of the value of $h$ where the graphs intersect?

A fashion company selected $100$ $12$-year-old boys and $100$ $12$-year-old girls to audition as models. The heights, $h \mathrm{cm}$, of the selected children are represented in the following graph.

The shortest $75$ boys and tallest $75$ girls were recalled for a second audition. On a cumulative frequency graph, show the heights of the children who were not recalled.

The following table shows the ages of the students currently at a university, given by percentage. Ages are rounded down to the number of whole years.

Represent the data in a percentage cumulative frequency polygon.

The following table shows the ages of the students currently at a university, given by percentage. Ages are rounded down to the number of whole years.

Represent the data in a percentage cumulative frequency polygon.

The oldest $8\%$of these students qualify as 'mature'. Use your polygon to estimate the minimum age requirement for a student to be considered mature. Give your answer to the nearest month.