The values of $x$ shown in the following table are to be represented in a bar chart.

$x$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
Frequency	$2$	$5$	$9$	$10$	$9$	$5$	$2$

If, instead, the two largest values of $x$ (i.e. $11$ and $11$) are changed to $-9$ and $b,$ so that the mean of $x$ decreases by $1,$ find the value of $b$ and investigate the effect that this has on the mode, the median and the shape of the curve.

Students' marks in a Biology examination are shown by percentage in the following table.

Without drawing an accurate histogram, describe the shape of the set of marks. What does the shape suggest about the values of the mean, the median and the mode?

Students' marks in a Biology examination are shown by percentage in the following table.

Information is provided about the marks in examinations in two other subjects:

Chemistry: mode $>$ median $>$ mean

Physics: mean $>$ median $>$ mode

Sketch a curve to show the shape of the distribution of marks in each of these exams.

For each of the following sets of data, decide whether you would expect the mean to be less than, equal to or greater than the median and the mode.

The ages of patients receiving long-term care at a hospital.

For each of the following sets of data, decide whether you would expect the mean to be less than, equal to or greater than the median and the mode.

The numbers of goals scored in football matches.

For each of the following sets of data, decide whether you would expect the mean to be less than, equal to or greater than the median and the mode.

The heights of adults living in a particular city.

Nine values are $7, 13, 28, 36, 13, 29, 31, 13$ and $x.$

Write down the value of the measure of central tendency that can be found without knowing the value of $x.$