The following cumulative frequency graph shows the masses, $m$ grams, of $152$ uncut diamonds.

The lightest $40$ diamonds are classified as small. The heaviest $40$ diamonds are classified as large. Estimate the difference between the mass of the heaviest small diamond and the lightest large diamond.

The following cumulative frequency graph shows the masses, $m$ grams, of $152$ uncut diamonds.

The point marked at $P(24,152)$ on the graph indicates that the $152$ uncut diamonds all have masses of less than $24$ grams.
Each diamond is now cut into two parts of equal mass. Assuming that there is no wastage of material, write down the coordinates of the point corresponding to $P$ on a cumulative frequency graph representing the masses of these cut diamonds.

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

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

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.