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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 to represent these data, indicating clearly any outliers.
Answer
To construct the box plot, we first calculate the interquartile range (IQR):
Next, we determine the lower and upper limits for identifying outliers:
- Lower limit = Q1 - 1.5 * IQR = 7 - 1.5 * 7 = -3.5
- Upper limit = Q3 + 1.5 * IQR = 14 + 1.5 * 7 = 24.5
Since the highest value, 25, is greater than 24.5, it is considered an outlier.
The box plot will include the following components:
- Minimum value: 3
- Lower quartile (Q1): 7
- Median: 12
- Upper quartile (Q3): 14
- Maximum value (excluding outlier): 20
- Indicate outlier: 25 above the box.
Place this data on the graph provided.
Step 2
State the skewness of the distribution of the amount of sales received. Justify your answer.
Answer
The skewness of the distribution is negatively skewed. This is because the median (12) is less than the upper quartile (14) and the lower quartile (7). The presence of the outlier (25) also pulls the data in a way that indicates a longer tail on the left side of the distribution.
Step 3
Comment on the claim that for 75% of the months, the amount received per month is greater than £10000.
Answer
This claim is not true. From the data, the lower quartile (Q1) is 7, which corresponds to £7000. This indicates that 75% of the months fall below £7000. Therefore, the statement that 75% of the months have sales greater than £10000 is incorrect.