6 During January the numbers of people entering a store during the first hour after opening were as follows.
| Time after opening, | | \(x\) minutes |
| Frequency | |
| \(0 < x \leqslant 10\) | 210 | 210 |
| \(10 < x \leqslant 20\) | 134 | 344 |
| \(20 < x \leqslant 30\) | 78 | 422 |
| \(30 < x \leqslant 40\) | 72 | \(a\) |
| \(40 < x \leqslant 60\) | \(b\) | 540 |
- Find the values of \(a\) and \(b\).
- Draw a cumulative frequency graph to represent this information. Take a scale of 2 cm for 10 minutes on the horizontal axis and 2 cm for 50 people on the vertical axis.
- Use your graph to estimate the median time after opening that people entered the store.
- Calculate estimates of the mean, \(m\) minutes, and standard deviation, \(s\) minutes, of the time after opening that people entered the store.
- Use your graph to estimate the number of people entering the store between ( \(m - \frac { 1 } { 2 } s\) ) and \(\left( m + \frac { 1 } { 2 } s \right)\) minutes after opening.