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The box plot in Figure 1 shows a summary of the weights of the luggage, in kg, for each musician in an orchestra on an overseas tour - Edexcel - A-Level Maths Statistics - Question 2 - 2007 - Paper 2
Question 2
The box plot in Figure 1 shows a summary of the weights of the luggage, in kg, for each musician in an orchestra on an overseas tour. The airline's recommended weig... show full transcript
Worked Solution & Example Answer:The box plot in Figure 1 shows a summary of the weights of the luggage, in kg, for each musician in an orchestra on an overseas tour - Edexcel - A-Level Maths Statistics - Question 2 - 2007 - Paper 2
Step 1
state the proportion of the musicians whose luggage was below the recommended weight limit.
Answer
Looking at the box plot (Figure 1), the upper quartile is at approximately 54 kg. Since 25% of the musicians are charged for taking heavy luggage, we can conclude that 75% of the musicians' luggage is below 54 kg. Therefore, the proportion of musicians whose luggage is below the recommended weight limit of 45 kg is:
Step 2
Step 3
Explain what you understand by the + on the box plot in Figure 1, and suggest an instrument that the owner of this luggage might play.
Answer
The '+' on the box plot indicates an outlier or an extreme value in the distribution of luggage weights. It signifies that there is at least one musician whose luggage weight was significantly higher than the majority. An instrument that the owner might play could be a tuba, as it is one of the heaviest instruments typically carried by musicians.
Step 4
Describe the skewness of this distribution. Give a reason for your answer.
Answer
The distribution appears to be positively skewed, as indicated by the longer tail on the right side of the box plot. This suggests that there are some musicians with significantly heavier luggage, as seen in the presence of outliers.
Step 5
Find the standard deviation of this normal distribution.
Answer
To find the standard deviation of the luggage weights that are assumed to be normally distributed, we use the values from the box plot. The standard deviation can be calculated as:
From the box plot, the calculated value for the standard deviation is approximately 1.43 kg.