Photo AI
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 Stem | Leaf -... 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
Step 2
Find (b) the interquartile range.
Answer
To find the interquartile range (IQR), first determine the first (Q1) and third quartiles (Q3).
-
The first quartile (Q1) is the median of the first half of the data (scores below the median): 0, 7, 1, 8, 2, 4, 4, 3, 2. Therefore, Q1 = 24.
-
The third quartile (Q3) is the median of the second half of the data (scores above the median): 4, 5, 9, 4, 0, 0, 0, 0. Thus, Q3 = 40.
Now we can calculate the IQR: IQR = Q3 - Q1 = 40 - 24 = 16.
Step 3
Find (c) Explain why there is only one employee who will undergo retraining.
Answer
To determine outliers, calculate Q1 - 1.0 * IQR. This gives: Q1 - IQR = 24 - 16 = 8.
An outlier is any score below this value. The scores are: 0, 7, 1, 8, 2, 4, 4, 3, 2, 3, 3, 4, 5, 9, 4, 0, 0, 0, 0.
Only the score of 7 is below 8. Thus, only one employee (the one who scored 7) will undergo retraining.
Step 4
Find (d) On the graph paper on page 5, draw a box plot to illustrate the employees’ scores.
Answer
To draw the box plot, mark the below points:
- Minimum score: 0
- Q1: 24
- Median: 33
- Q3: 40
- Maximum score: 48
Draw a box from Q1 to Q3 with a line at the median. Add "whiskers" extending to the minimum and maximum values. The outlier (7) should also be marked appropriately.