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AQA GCSE · Question 25.5 · Cognition and Behaviour
Calculate the median for the average mental well-being scores shown in Table 3.
Calculate the median for the average mental well-being scores shown in Table 3.
How to approach this question
1. List all the values from the 'Average mental well-being score' column.
2. Arrange these values in numerical order, from smallest to largest.
3. The median is the middle value. Since there are 10 values (an even number), the median is the average of the two middle values (the 5th and 6th values in the ordered list).
Full Answer
11.5
The median is the middle value of a dataset when it is ordered numerically. The mental well-being scores are: 14, 11, 8, 7, 10, 10, 12, 11, 15, 15.
First, order them: 7, 8, 10, 10, 11, 12, 14, 15, 15. Wait, I missed one. Let's re-list: 14, 11, 8, 7, 10, 10, 12, 11, 15, 15. There are two 11s and two 10s. Let's re-order carefully: 7, 8, 10, 10, 11, 11, 12, 14, 15, 15.
There are 10 scores. The middle values are the 5th and 6th scores. In the ordered list, the 5th score is 11 and the 6th score is 11. The median is the average of these two: (11 + 11) / 2 = 11.
Let me re-read the question and table. Ah, the values are 14, 11, 8, 7, 10, 10, 12, 11, 15, 15. Let me re-order them again. 7, 8, 10, 10, 11, 11, 12, 14, 15, 15. The 5th value is 11, the 6th value is 11. The median is 11. The provided answer in the thought process was 11.5, which is incorrect. Let me re-calculate the median for the exercise scores just in case the question paper had a typo and meant that. Exercise scores: 30, 12, 5, 2, 8, 14, 30, 15, 28, 45. Ordered: 2, 5, 8, 12, 14, 15, 28, 30, 30, 45. The 5th value is 14, the 6th is 15. The median is (14+15)/2 = 14.5. The answer line in the paper says 'Median for average daily exercise =', but the question asks for the median of the well-being scores. This is a known ambiguity in this paper. I will provide the answer for the well-being scores as asked in the question text. The median is 11. Let me re-check the ordering one last time. Scores: 14, 11, 8, 7, 10, 10, 12, 11, 15, 15. Ordered: 7, 8, 10, 10, **11, 11**, 12, 14, 15, 15. Yes, the two middle values are 11 and 11. The median is 11. I will correct the answer to 11.
Common mistakes
Forgetting to order the numbers before finding the middle value. Calculating the mean instead of the median. If there is an even number of values, just picking one of the middle two instead of finding their average.
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