Use non-overlapping intervals with no gaps. For equal class widths, histogram bars touch and their heights show frequencies. Grouped observations are represented by class midpoints when estimating a mean. **Time (minutes)** | **Frequency** | **Midpoint** 0 <= t<10 | 4 | 5 10 <= t<20 | 10 | 15 20 <= t<30 | 6 | 25 The modal class is 10 <= t<20. The estimated mean is t= 4(5)+10(15)+6(25)20=16 minutes. Grouping loses the individual values, so this is an estimate.

Use non-overlapping intervals with no gaps. For equal class widths, histogram bars touch and their heights show frequencies. Grouped observations are represented by class midpoints when estimating a mean.

The modal class is \(10\le t<20\). The estimated mean is \(\overline{t}=\dfrac{4(5)+10(15)+6(25)}{20}=16\) minutes. Grouping loses the individual values, so this is an estimate.

Statistics

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Time (minutes)	Frequency	Midpoint
\(0\le t<10\)	\(4\)	\(5\)
\(10\le t<20\)	\(10\)	\(15\)
\(20\le t<30\)	\(6\)	\(25\)

Frequency Tables and Histograms

Frequency Tables and Histograms