7. The following table gives the weights, in grams, of 60 items delivered to a company in a day.
| Weight (g) | \(0 - 10\) | \(10 - 20\) | \(20 - 30\) | \(30 - 40\) | \(40 - 50\) | \(50 - 60\) | \(60 - 80\) |
| No. of items | 2 | 11 | 18 | 12 | 9 | 6 | 2 |
- Use interpolation to calculate estimated values of (i) the median weight,
(ii) the interquartile range,
(iii) the thirty-third percentile.
Outliers are defined to be outside the range from \(2 \cdot 5 Q _ { 1 } - 1 \cdot 5 Q _ { 3 }\) to \(2 \cdot 5 Q _ { 3 } - 1 \cdot 5 Q _ { 1 }\). - Given that the lightest item weighed 3 g and the two heaviest weighed 65 g and 79 g , draw on graph paper an accurate box-and-whisker plot of the data. Indicate any outliers clearly.
- Describe the skewness of the distribution.
The mean weight was 32.0 g and the standard deviation of the weights was 14.9 g .
- State, with a reason, whether you would choose to summarise the data by using the mean and standard deviation or the median and interquartile range.
On another day, items were delivered whose weights ranged from 14 g to 58 g ; the median was 32 g , the lower quartile was 24 g and the interquartile range was 26 g .
- Draw a further box plot for these data on the same diagram. Briefly compare the two sets of data using your plots.
( 6 marks)