2. The age in years of the residents of two hotels are shown in the back to back stem and leaf diagram below.
Abbey Hotel \(8 | 5 | 0\) means 58 years in Abbey hotel and 50 years in Balmoral hotel Balmoral Hotel
| (1) | 2 | 0 | | |
| (4) | 9751 | 1 | | |
| (4) | 9831 | 2 | 6 | (1) |
| (11) | 99997665332 | 3 | 447 | (3) |
| (6) | 987750 | 4 | 005569 | (6) |
| \multirow[t]{3}{*}{(1)} | 8 | 5 | 000013667 | (9) |
| | 6 | 233457 | (6) |
| | 7 | 015 | (3) |
For the Balmoral Hotel,
- write down the mode of the age of the residents,
- find the values of the lower quartile, the median and the upper quartile.
- Find the mean, \(\bar { x }\), of the age of the residents.
- Given that \(\sum x ^ { 2 } = 81213\) find the standard deviation of the age of the residents.
One measure of skewness is found using
$$\frac { \text { mean - mode } } { \text { standard deviation } }$$
- Evaluate this measure for the Balmoral Hotel.
For the Abbey Hotel, the mode is 39 , the mean is 33.2 , the standard deviation is 12.7 and the measure of skewness is - 0.454
- Compare the two age distributions of the residents of each hotel.