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The box plot shows information about the distribution of the amounts of money spent by some male students on their holidays - Edexcel - GCSE Maths - Question 9 - 2017 - Paper 3
Question 9
The box plot shows information about the distribution of the amounts of money spent by some male students on their holidays. (a) Work out the interquartile range fo... show full transcript
Worked Solution & Example Answer:The box plot shows information about the distribution of the amounts of money spent by some male students on their holidays - Edexcel - GCSE Maths - Question 9 - 2017 - Paper 3
Step 1
Work out the interquartile range for the amounts of money spent by these male students.
Answer
To find the interquartile range (IQR), we start by determining the lower quartile (LQ) and upper quartile (UQ) values from the box plot. From the box plot, we observe:
- Lower Quartile (LQ) = 180 £
- Upper Quartile (UQ) = 350 £
The interquartile range can be calculated using the formula:
Thus, the interquartile range for the amounts of money spent by these male students is £170.
Step 2
On the grid above, draw a box plot for the information in the table.
Answer
To draw a box plot based on the provided values, we need to identify the key points: smallest, lower quartile, median, upper quartile, and largest values. The values are:
- Smallest = 60 £
- Lower quartile = 180 £
- Median = 300 £
- Upper quartile = 350 £
- Largest = 650 £
Using these values, the box plot is created as follows:
- Draw a number line to represent the range of money spent.
- Mark the smallest value (60 £) and the largest value (650 £).
- Draw a box from the lower quartile (180 £) to the upper quartile (350 £).
- Inside the box, indicate the median (300 £) with a line.
- Extend lines (whiskers) from both ends of the box to the smallest and largest values. (Note: The actual drawing of the box plot is not provided, as it's a graphical representation.)
Step 3
Is Chris correct? Give a reason for your answer.
Answer
Yes, Chris is correct. The box plots indicate the median values of the amounts spent by each group. For the male students, the median is 230 £ (which can be derived from the box plot). For the female students, the median is 300 £ as given in the table. Since 300 £ (female students) is greater than 230 £ (male students), it can be concluded that female students spent more money than male students. Therefore, Chris’s statement holds true.