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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. (b) 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 using the cumulative frequency graph, we first identify the midpoint of the data. Since there are 60 potatoes, the median is the weight corresponding to the 30th data point. We locate the cumulative frequency of 30 on the vertical axis and trace horizontally to the curve. From there, we drop down to the x-axis to find the estimated weight, which is approximately 57 g.
Step 2
Is Jamil correct? You must give a reason for your answer.
Answer
Jamil is not correct. The range of a dataset is calculated using the formula:
Jamil states that 80 – 40 – 40 gives a range of 40 g. However, if we assume the minimum weight is less than 40 g (as indicated by the cumulative frequency graph), then the maximum could indeed be 80 g, making the actual range possibly greater than 40 g.
Step 3
Show that less than 25% of the potatoes have a weight greater than 65 g.
Answer
To demonstrate that less than 25% of the potatoes weigh more than 65 g, we first find the cumulative frequency for weights greater than 65 g. From the graph, we observe that at 65 g, the cumulative frequency is approximately 47. Therefore, the number of potatoes weighing more than 65 g is:
Calculating the percentage:
Since 21.67% is less than 25%, we conclude that less than 25% of the potatoes have a weight greater than 65 g.