Measurements of the distances, $x \mathrm{mm}$, between two moving parts inside car engines were recorded and are summarised in the following table. There were $156$ engines of type $A$ and $156$ engines of type $B$.

Distance $\left(x\mathrm{mm}\right)$	$x<0.10$	$x<0.35$	$x<0.60$	$x<0.85$	$x<1.20$
Engine $A\left(cf\right)$	$0$	$16$	$84$	$144$	$156$
Engine $B\left(cf\right)$	$0$	$8$	$62$	$120$	$156$

 

Draw and label two cumulative frequency curves on the same axes.

Both types of engine must be repaired if the distance between these moving parts is more than a certain fixed amount. Given that $16$ type $A$ engines need repairing, estimate the number of type $B$ engines that need repairing.

The diameters, $d \mathrm{cm}$, of $60$ cylindrical electronic components are represented in the following cumulative frequency graph.

                                                                Diameter $(d \mathrm{cm})$

Find the number of components such that $0.2⩽d<0.4$, and explain why your answer is not an estimate.

The diameters, $d \mathrm{cm}$, of $60$ cylindrical electronic components are represented in the following cumulative frequency graph.

                                                                Diameter $(d \mathrm{cm})$

Estimate the number of components that have:
a diameter of less than $0.15 \mathrm{cm}$

The diameters, $d \mathrm{cm}$, of $60$ cylindrical electronic components are represented in the following cumulative frequency graph.

                                                                Diameter $(d \mathrm{cm})$

Estimate the number of components that have:
a radius of $0.16 \mathrm{cm}$ or more.

The diameters, $d \mathrm{cm}$, of $60$ cylindrical electronic components are represented in the following cumulative frequency graph.

                                                                Diameter $(d \mathrm{cm})$

Estimate the value of $k$, given that $20\%$ of the components have diameters of $k$ $\mathrm{mm}$ or more.

The diameters, $d \mathrm{cm}$, of $60$ cylindrical electronic components are represented in the following cumulative frequency graph.

                                                                Diameter $(d \mathrm{cm})$

Give the reason why $0.1-0.2 \mathrm{cm}$ is the modal class.

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

Estimate the number of uncut diamonds with masses such that:

$9⩽m<17$

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

Estimate the number of uncut diamonds with masses such that:

$7.2⩽m<15.6$.

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.