7 In a UK government survey in 2000, smokers were asked to estimate the time between their waking and their having the first cigarette of the day. For heavy smokers, the results were as follows.
| Time between waking | | and first cigarette |
| | | | | |
| Percentage of smokers | 31 | 27 | 19 | 14 | 9 |
Times are given correct to the nearest minute.
- Assuming that 'At least 60 minutes' means 'At least 60 minutes but less than 240 minutes', calculate estimates for the mean and standard deviation of the time between waking and first cigarette for these smokers.
- Find an estimate for the interquartile range of the time between waking and first cigarette for these smokers. Give your answer correct to the nearest minute.
- The meaning of 'At least 60 minutes' is now changed to 'At least 60 minutes but less than 480 minutes'. Without further calculation, state whether this would cause an increase, a decrease or no change in the estimated value of
(a) the mean,
(b) the standard deviation,
(c) the interquartile range.