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The box plot shows information about the length of time, in minutes, some people waited to see a doctor at a hospital on Monday - Edexcel - GCSE Maths - Question 10 - 2021 - Paper 2
Question 10
The box plot shows information about the length of time, in minutes, some people waited to see a doctor at a hospital on Monday. (a) Work out the interquartile rang... show full transcript
Worked Solution & Example Answer:The box plot shows information about the length of time, in minutes, some people waited to see a doctor at a hospital on Monday - Edexcel - GCSE Maths - Question 10 - 2021 - Paper 2
Step 1
Work out the interquartile range of the information in the box plot.
Answer
To find the interquartile range (IQR), we need to subtract the lower quartile (LQ) from the upper quartile (UQ).
From the box plot, the lower quartile (LQ) is observed at the 50-minute mark and the upper quartile (UQ) is at 140 minutes. Therefore, we can calculate the IQR as:
Step 2
Is Becky correct? Explain why.
Answer
Becky is incorrect.
The median, as indicated in the table, is 100 minutes, which means that 50% of the waiting times are below this value. Since 2 hours corresponds to 120 minutes, this implies that not all individuals waited for 2 hours or longer. In fact, individuals waited for a duration that is less than 2 hours in at least half of the cases. Thus, Becky’s statement is inaccurate.
Step 3
Give one reason why Becky may be wrong.
Answer
One possible reason Becky may be wrong is that the median waiting time for Tuesday is 100 minutes, whereas the interquartile range shows that many individuals likely waited less than this duration. The distribution of times could be different, with a possibility that not all waited longer on Tuesday. The range for Tuesday indicates that fewer people are waiting longer than the median time compared to Monday.