Mean $\text{mean}=\dfrac{\text{sum of values}}{\text{how many}}$add them all up, then divide by how many there are
Median $\text{middle value}$ORDER the values first, then take the middle (or the mean of the middle two)
Mode $\text{most common}$the value that appears most often; there can be none or more than one
Range $\text{highest}-\text{lowest}$a measure of SPREAD, not an average
Estimated mean (grouped) $\dfrac{\sum(\text{midpoint}\times f)}{\sum f}$use the midpoint of each class as the value
From a list · $3,\ 7,\ 7,\ 2,\ 6$
mean $=\dfrac{25}{5}=5$; range $=7-2=5$
order $2,3,6,7,7$: median $=6$, mode $=7$
Median (even) · $2,\ 4,\ 7,\ 9$
ordered already; middle two are $4$ and $7$
median $=\dfrac{4+7}{2}=5.5$
Missing value · mean of $4$ numbers is $6$
sum $=6\times4=24$
subtract the known three to find the fourth
Mean: the total shared out equally: sum ÷ how many.
Median: the middle value once the data is in order.
Mode: the most common value (the modal value).
Range: highest − lowest; how spread out the data is.
Outlier: a value much bigger or smaller than the rest; it affects the MEAN most.
✗ Taking the median without ordering the list
✓ order smallest-to-largest first, then take the middle.
✗ Median of an even list $=$ the two middle values
✓ take the MEAN of the two middle values.
✗ Range $=$ how many values there are
✓ range $=$ highest $-$ lowest value.
✗ Grouped mean $\div$ number of classes
✓ divide $\sum(\text{midpoint}\times f)$ by the total FREQUENCY.
• Always ORDER the data before finding the median.
• The range is a measure of spread, NOT an average.
• For grouped data you can only ESTIMATE the mean (use class midpoints).
• Mean: add then divide. Median: order then middle. Mode: most common.
• A missing value: total $=$ mean $\times$ how many, then subtract the ones you know.
• The mode is the only average that works for non-number data (e.g. colours).
mathedup.co.uk · sheet CHNP