Spread and grouped data
Grouped data (Extended)
- For grouped data you can't find the exact mean — estimate it using the midpoint of each group as the value.
- The modal class is just the group with the highest frequency.
- Worked example: the class $10$ to $20$ has midpoint $\tfrac{10+20}{2}=15$.
Practice
A grouped class runs from 10 to 20. What midpoint do you use as its value?
(10 + 20)/2 = 15.
Quartiles and IQR (Extended)
- Put the data in order. The quartiles cut it into four equal parts: lower quartile (LQ) at $\tfrac14$, upper quartile (UQ) at $\tfrac34$.
- The interquartile range measures the middle half:
$$\text{IQR} = \text{UQ} - \text{LQ}$$
- It is useful because it ignores extreme values.
Practice
A data set has upper quartile 15 and lower quartile 7. Find the interquartile range.
IQR = UQ − LQ = 15 − 7 = 8.
Practice
The interquartile range ignores extreme values, unlike the range.
The IQR uses only the middle half, so outliers do not affect it.
You've got it
Key idea
- estimate a grouped mean using each class midpoint; modal class = highest frequency
- IQR $= \text{UQ} - \text{LQ}$ (spread of the middle half)
- the IQR ignores extreme values, unlike the range