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The cumulative frequency graph shows information about the weights of 60 potatoes - Edexcel - GCSE Maths - Question 11 - 2017 - Paper 3
Question 11
The cumulative frequency graph shows information about the weights of 60 potatoes. (a) Use the graph to find an estimate for the median weight. Jamil says, "80 - ... show full transcript
Worked Solution & Example Answer:The cumulative frequency graph shows information about the weights of 60 potatoes - Edexcel - GCSE Maths - Question 11 - 2017 - Paper 3
Step 1
Use the graph to find an estimate for the median weight.
Answer
To find the median weight, we need to locate the point on the cumulative frequency graph corresponding to half of the total number of potatoes. Since there are 60 potatoes, we look for the cumulative frequency of 30. From the graph, we can determine the weight at this point, which is approximately 57 g. Therefore, the estimated median weight is 57 g.
Step 2
Is Jamil correct? You must give a reason for your answer.
Answer
Jamil's statement might not be correct because the range is computed as the maximum weight minus the minimum weight. However, since we do not have explicit values for the maximum weight or the minimum weight from the graph, we cannot confirm his calculation. The minimum weight could be less than 40 g, which would affect the range.
Step 3
Show that less than 25% of the potatoes have a weight greater than 65 g.
Answer
To show that less than 25% of the potatoes weigh more than 65 g, we first determine 25% of 60, which is 15. We check the cumulative frequency graph at 65 g, which indicates that approximately 45 potatoes weigh 65 g or less. Therefore, the number of potatoes weighing more than 65 g is 60 - 45 = 15. Since 15 potatoes is exactly 25% of the total, we can conclude that less than 25% of the potatoes weigh greater than 65 g.