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The table shows some information about the dress sizes of 25 women - Edexcel - GCSE Maths - Question 3 - 2017 - Paper 3
Question 3
The table shows some information about the dress sizes of 25 women. | Dress size | Number of women | |------------|------------------| | 8 | 2 ... show full transcript
Worked Solution & Example Answer:The table shows some information about the dress sizes of 25 women - Edexcel - GCSE Maths - Question 3 - 2017 - Paper 3
Step 1
Find the median dress size.
Answer
To determine the median dress size, we need to arrange the dress sizes from the table according to the number of women.
The dress sizes and their frequencies are:
- Size 8: 2 women
- Size 10: 9 women
- Size 12: 8 women
- Size 14: 6 women
Arranging these sizes based on frequency:
- Size 8: 8, 8
- Size 10: 10, 10, 10, 10, 10, 10, 10, 10, 10
- Size 12: 12, 12, 12, 12, 12, 12, 12, 12
- Size 14: 14, 14, 14, 14, 14, 14
Thus, the complete sequence of dress sizes is: 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 14, 14, 14, 14, 14, 14.
As there are 25 women (an odd number), the median is the 13th value in this ordered list, which is 12.
Step 2
Is Zoe correct?
Answer
Zoe's assertion is incorrect. When calculating the probability of either event occurring, we must ensure that the events are mutually exclusive. In this case, the shoe size of 7 and the dress size of 14 are independent events; thus, we cannot simply add the probabilities. Instead, we should assess if any overlap exists. Since there's no context given to suggest that one woman could count in both categories simultaneously, we cannot assume they are mutually exclusive. Hence, the correct probability should consider that a woman chosen could only fall into one category or the other, leading to potential miscalculation in Zoe's reasoning.