6. The labelling on bags of garden compost indicates that the bags weigh 20 kg . The weights of a random sample of 50 bags are summarised in the table below.
| Weight in kg | Frequency |
| 14.6-14.8 | 1 |
| 14.8-18.0 | 0 |
| 18.0-18.5 | 5 |
| 18.5-20.0 | 6 |
| 20.0-20.2 | 22 |
| 20.2-20.4 | 15 |
| 20.4-21.0 | 1 |
- On graph paper, draw a histogram of these data.
- Using the coding \(y = 10\) (weight in \(\mathrm { kg } - 14\) ), find an estimate for the mean and standard deviation of the weight of a bag of compost.
[0pt]
[Use \(\Sigma f y ^ { 2 } = 171\) 503.75] - Using linear interpolation, estimate the median.
The company that produces the bags of compost wants to improve the accuracy of the labelling. The company decides to put the average weight in kg on each bag.
- Write down which of these averages you would recommend the company to use. Give a reason for your answer.