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The 19 employees of a company take an aptitude test - Edexcel - A-Level Maths Statistics - Question 2 - 2010 - Paper 1
Question 2
The 19 employees of a company take an aptitude test. The scores out of 40 are illustrated in the stem and leaf diagram below: 2|6 means a score of 26 0 | 7 ... show full transcript
Worked Solution & Example Answer:The 19 employees of a company take an aptitude test - Edexcel - A-Level Maths Statistics - Question 2 - 2010 - Paper 1
Step 1
(a) the median score.
Answer
To find the median score, first list all the scores derived from the stem-and-leaf diagram in ascending order:
- Scores: 7, 18, 24, 26, 26, 33, 33, 34, 35, 39, 40, 40, 40, 0, 0
Since there are 19 scores (an odd number), the median is the middle value, which is the 10th score in the ordered list. Thus, the median score is 33.
Step 2
(b) the interquartile range.
Answer
To determine the interquartile range (IQR), we first find the first quartile (Q1) and the third quartile (Q3).
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First Quartile (Q1): Q1 is the median of the first half of the data (the first 10 scores): Scores: 7, 18, 24, 26, 26 The median (Q1) of this half is 24.
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Third Quartile (Q3): Q3 is the median of the second half of the data (the last 10 scores): Scores: 33, 33, 34, 35, 39, 40, 40, 40, 0, 0 The median (Q3) of this half is 40.
Finally, we calculate the IQR as follows:
Step 3
(c) Explain why there is only one employee who will undergo retraining.
Answer
To determine the outliers, we apply the outlier formula:
An outlier is anyone with a score less than:
From the scores listed earlier, only the score of 7 is less than 8. Therefore, only one employee who scored 7 will be considered an outlier and undergo retraining.
Step 4
(d) On the graph paper on page 5, draw a box plot to illustrate the employees’ scores.
Answer
To draw the box plot:
- Determine the minimum score (7), Q1 (24), median (33), Q3 (40), and maximum score (40).
- Draw a number line, marking these values.
- Draw a box from Q1 to Q3, with a line at the median.
- Extend 'whiskers' to the minimum score and maximum score. Ensure to mark the outlier (if applicable). Your plot should clearly show the distribution of the scores.