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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 11 - 2021 - Paper 2
Question 11
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 11 - 2021 - Paper 2
Step 1
Work out the interquartile range of the information in the box plot.
Answer
To calculate the interquartile range (IQR), we subtract the lower quartile (Q1) from the upper quartile (Q3). According to the box plot:
- Lower quartile (Q1) is at 50 minutes.
- Upper quartile (Q3) is at 188 minutes.
Thus, the IQR can be calculated as follows:
The interquartile range of the information in the box plot is 138 minutes.
Step 2
Is Becky correct? Explain why.
Answer
Yes, Becky is correct, with reason.
The statement made by Becky states that "50% of the people waited for at least 2 hours."
However, given that:
- The median waiting time is 100 minutes, which is equivalent to 1 hour and 40 minutes.
- 50% of the people are below the median waiting time.
- Since 100 minutes is less than 120 minutes (2 hours), Becky is indeed mistaken in her assertion.
Step 3
Give one reason why Becky may be wrong.
Answer
One reason why Becky may be wrong is that the distribution of waiting times on Tuesday could vary compared to Monday. The data provided shows that the upper quartile waiting time on Tuesday is at 140 minutes, while on Monday it is significantly higher, leading to the assumption that potentially fewer people experienced longer waiting times on Tuesday. Therefore, her comparison might not accurately reflect the waiting times on both days.