In the 1920s Edward Filbert became the tenant of Kings Farm in Cambridge shire. In 1978 his grandson James Filbert became the latest manager. But in the intervening years the farm has changed considerably. It has grown from 195 acres to over 3,000 acres and is owned by an agricultural company that owns several other farms in the area. Kings Farm grows a variety of vegetables, cereals and fruit, with Kings Fruit Farm as a subsidiary that focuses on their apple, pear, plum, damson and cherry orchards.Recently James has been looking at the sales of plums. These are graded and sold as fruit to local shops and markets, for canning to a local cannery, or for jam to a more distant processor. The plums sold for canning earn about half as much income as those sold for fruit, but twice as much as those sold for jam.James is trying to estimate the weight of plums sold each year. He does not know this, as the plums are sold by the basket rather than by weight, with each basket holding about 25 kg of plums. For a pilot study, James set up some scales to see whether he could weigh the amount of fruit in a sample of baskets. On the first day he weighed 10 baskets, six of which were sold as fruit, three for canning and one for jam. The weights of fruit, in kilograms, were as follows:25.6 20.8 29.4 28.0 22.2 23.1 25.3 26.5 20.7 21.9This trial seemed to work, so James then weighed a sample of 50 baskets on three consecutive days. The weights of fruit, in kg, were as follows:
He also recorded the number of each sample sent to each destination:
Pickers are paid by the basket, and the payments book showed the number of baskets picked on the three days as 820, 750 and 700 respectively. During a good harvest, a total of around 6,000 baskets are picked.Questions• What information can James find from these figures? How can he use this information?• How should he set about a complete survey of the fruit crop?