The times, to the nearest minute, of 150 athletes taking part in a charity run are recorded. The results are summarised in the table.
| Time (minutes) |
101–120 |
121–130 |
131–135 |
136–145 |
146–160 |
| Frequency |
18 |
48 |
34 |
32 |
18 |
Draw a histogram to represent this information.
Solution
To draw the histogram, calculate the frequency density for each class interval using the formula:
\(\text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Width}}\)
Class widths are: 20, 10, 5, 10, 15.
Calculate frequency densities:
\(\frac{18}{20} = 0.9\)
\(\frac{48}{10} = 4.8\)
\(\frac{34}{5} = 6.8\)
\(\frac{32}{10} = 3.2\)
\(\frac{18}{15} = 1.2\)
Draw bars with these heights on the histogram, ensuring the axes are labeled with 'Frequency Density' and 'Time in minutes'.
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