For the data shown in the following table, $x$ has a mean of $7.15.$

$x$	$3$	$6$	$10$	$15$
Frequency	$a$	$b$	$c$	$d$

Find the mean value of $y$ given in the following table.

$y$	$11$	$14$	$18$	$23$
Frequency	$a$	$b$	$c$	$d$

For the data shown in the following table, $x$ has a mean of $7.15.$

Find a calculated estimate of the mean value of $z$ given in the following table.

The table below shows the number of books read last month by a group of children.

If the mean number of books read is exactly $3.75,$ find the value of $q.$

The table below shows the number of books read last month by a group of children.

Find the greatest possible value of $q$ if: the modal number of books read is $4$

The table below shows the number of books read last month by a group of children.

Find the greatest possible value of $q$ if: the median number of books read is $4.$

The following table gives the heights, to the nearest $5 \mathrm{cm},$ of a group of people.

Given that the modal class is $140-150 \mathrm{cm},$ find the least possible value of $p.$

The following histogram illustrates the masses, $m$ kilograms, of the $216$ sales of hay that a farmer made to customers last year.

Show that a calculated estimate of the mean is equal to the median.

The following histogram illustrates the masses, $m$ kilograms, of the $216$ sales of hay that a farmer made to customers last year.

Estimate the price per kilogram at which the hay was sold, given that these sales generated exactly $\$1944.$ Why is it possible that none of the customers actually paid this amount per kilogram for the hay?

An Internet service provider wants to know how customers rate its services. A questionnaire asks customers to tick one of the following boxes excellent, good, average, poor, very poor

How might the company benefit from knowing each of the available average responses of its customers?