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Over a long period of time a small company recorded the amount it received in sales per month - Edexcel - A-Level Maths Statistics - Question 3 - 2011 - Paper 1
Question 3
Over a long period of time a small company recorded the amount it received in sales per month. The results are summarised below. | Amount received in sales (£1000s)... show full transcript
Worked Solution & Example Answer:Over a long period of time a small company recorded the amount it received in sales per month - Edexcel - A-Level Maths Statistics - Question 3 - 2011 - Paper 1
Step 1
Draw a Box Plot and Identify Outliers
Answer
To construct the box plot, we first determine the necessary components:
- Lower Quartile (Q1): 7
- Median (Q2): 12
- Upper Quartile (Q3): 14
Next, calculate the interquartile range (IQR):
Now, calculate the lower and upper outlier limits:
- Lower outlier limit = Q1 - 1.5 × IQR = 7 - 1.5 × 7 = -3.5
- Upper outlier limit = Q3 + 1.5 × IQR = 14 + 1.5 × 7 = 24.5
Since 25 (the highest value) exceeds the upper limit (24.5), it qualifies as an outlier.
The box plot will display the following:
- A box from Q1 (7) to Q3 (14).
- A line at the median (12).
- Whiskers extending to the two lowest values (3 and 4) and to the upper limit (20).
- An isolated point representing the outlier (25).
Indicate the outlier clearly on the diagram.
Step 2
State the Skewness of the Distribution
Answer
The skewness of a distribution can be assessed using the relative differences between the quartiles. Since:
which translates to:
This confirms that the data is negatively skewed. In a negatively skewed distribution, the left tail (lower values) is longer or fatter than the right tail, thus our conclusion is that the distribution has a negative skew.
Step 3
Comment on the Claim about Sales
Answer
The company claims that for 75% of the months, the amount received per month is greater than £10000. To evaluate this, we look at the quartile data. The lower quartile (Q1) is 7, indicating that 25% of the months had sales below £7000. Therefore, it can be concluded that:
- Since the median (Q2) is 12 (representing £12000), and also considering the upper limit of sales, it suggests that only 50% of the observed data lies above £10000.
- Consequently, 75% of the months cannot possibly exceed the claim of receiving more than £10000. Thus, the company's claim is not true.