Averages and spread Worked Solutions — GCSE Maths

Add up all of the values

The mean shares the total out equally, so the first job is the total. Adding the $6$ values gives $69$.

Count how many values there are

There are $6$ values in the list, so the total is shared between $6$.

Divide the total by the number of values

The mean is $69 \div 6 = 11.5$.

Add up all of the values

The mean shares the total out equally, so the first job is the total. Adding the $6$ values gives $99$.

Count how many values there are

There are $6$ values in the list, so the total is shared between $6$.

Divide the total by the number of values

The mean is $99 \div 6 = 16.5$.

Add up all of the values

The mean shares the total out equally, so the first job is the total. Adding the $7$ values gives $84$.

Count how many values there are

There are $7$ values in the list, so the total is shared between $7$.

Divide the total by the number of values

The mean is $84 \div 7 = 12$.

Add up all of the values

The mean shares the total out equally, so the first job is the total. Adding the $8$ values gives $106$.

Count how many values there are

There are $8$ values in the list, so the total is shared between $8$.

Divide the total by the number of values

The mean is $106 \div 8 = 13.25$.

Put the values in order, smallest first

The median is the middle value once the data is in order. Ordering the list first is what makes "middle" mean anything.

Find the position of the middle value

With $9$ values there is one value exactly in the middle: the $5$th one.

Read off the value in that position

Counting to the $5$th value in the ordered list gives $13$.