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Ali and Beth take it in turns to play a computer game - OCR - GCSE Maths - Question 13 - 2020 - Paper 1
Question 13
Ali and Beth take it in turns to play a computer game. On each turn, the player achieves a score out of 50. Ali and Beth play the computer game many times and record... show full transcript
Worked Solution & Example Answer:Ali and Beth take it in turns to play a computer game - OCR - GCSE Maths - Question 13 - 2020 - Paper 1
Step 1
Draw a box plot to show the distribution of Ali's scores.
Answer
To create a box plot for Ali's scores, we need to determine the relevant five-number summary:
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Minimum (Min): Given that the range is 23 and the highest score is 38, we calculate:
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Lower Quartile (Q1): Given as 24.
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Median (Q2): Given as 31.
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Upper Quartile (Q3): Since the interquartile range is 11, we calculate:
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Maximum (Max): Given as 38.
Now, we can plot these values on a number line from 0 to 50:
- The minimum score is 15.
- The lower quartile (25th percentile) is 24.
- The median (50th percentile) is 31.
- The upper quartile (75th percentile) is 35.
- The maximum score is 38.
The box plot will have:
- A box from Q1 (24) to Q3 (35).
- A line at the median (31) inside the box.
- Whiskers extending from 15 to 24 (left) and from 35 to 38 (right).
Step 2
Find the interquartile range of Beth's scores.
Answer
The interquartile range (IQR) can be found by subtracting the lower quartile from the upper quartile. Of Beth's scores, we will use the values represented in the box plot:
- Lower Quartile (Q1): (Refer to the box plot for the specific value approximately).
- Upper Quartile (Q3): (Refer to the box plot for the specific value approximately).
The formula used: Substituting the values:
Evaluate to find the IQR.
Step 3
Is his statement correct? Explain your reasoning.
Answer
Kareem's statement claims that Beth is more consistent than Ali due to having a lower median score. However, consistency in scores is often measured by the spread of the data rather than just the median value.
To evaluate consistency, we should consider the interquartile range and standard deviation, which reflect the variability of the scores. If Beth's interquartile range is smaller than Ali's, then she may indeed be more consistent despite having a lower median. Conversely, a higher IQR for Beth compared to Ali would indicate more variability in her scores, which isn't consistent.
In conclusion, without comparing both players’ interquartile ranges, we cannot definitively validate Kareem's statement based solely on their median scores.