Averages and range
The three averages and range
- mean $= \dfrac{\text{sum of values}}{\text{how many}}$; median = the middle value in order; mode = the most common value.
- range = largest $-$ smallest (how spread out the data is).
- Worked example: $4, 7, 7, 2, 5$ → ordered $2,4,5,7,7$. Mean $\tfrac{25}{5}=5$, median $5$, mode $7$, range $7-2=5$.
Practice
Find the mean of 4, 7, 7, 2, 5.
(4 + 7 + 7 + 2 + 5)/5 = 25/5 = 5.
Practice
Find the mode of 4, 7, 7, 2, 5.
7 appears most often.
Practice
Find the range of 4, 7, 7, 2, 5.
Largest − smallest = 7 − 2 = 5.
Mean from a frequency table
- When values come with frequencies:
$$\text{mean} = \frac{\sum (\text{value} \times \text{frequency})}{\sum \text{frequency}}$$
- Worked example: values $1,2,3$ with frequencies $4,5,1$ → $\dfrac{1(4)+2(5)+3(1)}{10} = \dfrac{17}{10} = 1.7$.
Practice
Values 1, 2, 3 occur with frequencies 4, 5, 1. Find the mean (1 dp).
(1·4 + 2·5 + 3·1)/(4+5+1) = 17/10 = 1.7.
You've got it
Key idea
- mean = total ÷ count; median = middle in order; mode = most common
- range = largest − smallest
- frequency-table mean $= \dfrac{\sum(\text{value}\times\text{freq})}{\sum \text{freq}}$