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
| 1 8... 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
the median score
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Answer
To find the median score, we must first list all the scores derived from the stem-and-leaf diagram:
7
18
24
24
26
33
33
33
34
35
35
39
40
40
40
40
With 19 scores, the median will be the 10th value when sorted:
Median = 33.
Step 2
the interquartile range
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Answer
To find the interquartile range (IQR), we first identify the lower quartile (Q1) and upper quartile (Q3):
Lower Quartile (Q1): The 5th score is 26.
Upper Quartile (Q3): The 15th score is 40.
Now, the interquartile range is calculated as:
IQR=Q3−Q1=40−26=14.
Step 3
Explain why there is only one employee who will undergo retraining
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Answer
We need to calculate the outlier threshold using:
Q1−1.0imesIQR=26−14=12
Any score below 12 is considered an outlier.
Looking at the scores, only one score, which is 7, is below this threshold:
So, 7 is the only outlier.
Step 4
On the graph paper on page 5, draw a box plot to illustrate the employees’ scores
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Answer
To create the box plot, one should identify:
Minimum Value: 7
Q1: 26
Median: 33
Q3: 40
Maximum Value: 40
The box plot will reflect these values as follows:
The box extends from Q1 (26) to Q3 (40).
The line inside the box represents the median (33).
The whiskers extend from the minimum (7) to Q1 and from Q3 to the maximum (40).
A correctly drawn box plot should clearly depict these statistical values.
