Ten items were selected from each of four sections at a supermarket. Details of the prices of those items, in dollars, on$1\mathrm{st}$ April and on $1\mathrm{st}$ June are shown in the following table.

	1st April		1st June
	Mean	SD	Mean	SD
Bakery	$2.50$	$0.40$	$2.25$	$0.36$
Household	$5.00$	$1.20$	$4.75$	$1.25$
Tinned food	$4.00$	$0.60$	$4.10$	$0.60$
Fruit and veg	$2.00$	$0.40$	$2.00$	$0.50$

For which section's items the following statements be true? Briefly explain your answers.

The total cost of the items did not change.

Ten items were selected from each of four sections at a supermarket. Details of the prices of those items, in dollars, on$1\mathrm{st}$ April and on $1\mathrm{st}$ June are shown in the following table.

For which section's items could each of the following statements be true? Briefly explain each of your answers.

The price of each item changed by the same amount.

Ten items were selected from each of four sections at a supermarket. Details of the prices of those items, in dollars, on$1\mathrm{st}$ April and on $1\mathrm{st}$ June are shown in the following table.

For which section's items could each of the following statements be true? Briefly explain each of your answers.

The proportional change in the price of each item was the same.

Three boys and seven girls are asked how much money they have in their pockets. The boys have $\$2.50$ each and the mean amount that the $10$ children have is $\$3.90.$

Show that the girls have a total of $\$31.50.$

Three boys and seven girls are asked how much money they have in their pockets. The boys have $\$2.50$ each and the mean amount that the $10$ children have is $\$3.90.$

Given that the seven girls have equal amounts of money, find the standard deviation of the amounts that the $10$ children have.

Jean Luc was asked to record the times of $20$athletes in a long distance race. He started his stopwatch when the race began and then went to sit in the shade, where he fell asleep. On waking, he found that $x$ athletes had already completed the race but he was able to record the times taken by all the others.

State the possible value(s) of $x$ if Jean Luc was able to use his data to calculate: the variance of the times taken by the $20$ athletes.

Jean Luc was asked to record the times of $20$athletes in a long distance race. He started his stopwatch when the race began and then went to sit in the shade, where he fell asleep. On waking, he found that $x$ athletes had already completed the race but he was able to record the times taken by all the others.

State the possible value $\left(s\right)$ of $x$ if Jean Luc was able to use his data to calculate:

the interquartile range of the times taken by the $20$ athletes.[Answer $0,1,2,3,4$ or $0,1,2,3$]