The table shows information about the number of apples produced by different trees in a season. Part a) Work out the number of apple trees that produce more than 200 apples. Zainab says that the range of the number of apples produced could be any integer from 201 to 399. Part b) Explain why Zainab is correct.
The table tells us that four trees produce between 101 and 200 apples, seven trees produce between 201 and 300 apples, eight trees produce between 301 and 400 apples, and finally one tree produce between 401 and 500 apples.
The first part of our question asks us to work out the number of trees that produced more than 200 apples. The bottom three rows of the table — 201 to 300, 301 to 400, and 401 to 500 apples — are all more than 200 apples. We, therefore, need to add seven, eight, and one, the three frequencies for these rows. Seven plus eight plus one is equal to 16. Therefore, 16 trees produced more than 200 apples.
The second part of our question discusses the range of the number of apples produced. The range is equal to the highest value minus the lowest value. In group frequency tables, each group is an interval values. This means that the one tree in our last group could have produced 401 apples. It could have produced 500 apples or any integer in between them. Therefore, the highest value is somewhere between 401 and 500.
In the same way, we know that the lowest value is between 101 and 200. The four trees in this group could have all produced a number of apples close to 101. They could have all been close to 200 or they could have been spread out across the group.
We can use these values to calculate the smallest and largest possible range. The smallest possible range is calculated by subtracting 200 from 401. This is equal to 201. The largest possible range is calculated by subtracting 101 from 500. This is equal to 399.
We can, therefore, say that Zainab is correct as the range of the number of apples produced could be any integer or whole number from 201 to 399.