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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
From the box plot in Figure 1, we can determine that 75% of the musicians' luggage measurements fall below the recommended weight limit of 45 kg. Therefore, the proportion of musicians whose luggage was below the limit is ( 0.75 ) or 75%.
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 + sign on the box plot represents an outlier or 'extreme value' in the dataset. It indicates that a musician's luggage weight is significantly higher than the rest. A possible instrument that the owner might play, which could contribute to such heavy luggage, is the double bass, known for its hefty physical build.
Step 4
Describe the skewness of this distribution. Give a reason for your answer.
Answer
The distribution of luggage weights appears to be slightly positively skewed. This is indicated by the longer tail on the right side of the box plot, suggesting that fewer musicians have weights significantly exceeding the median. The box plot supports this observation, as the median and interquartile range are closer to the lower end.
Step 5
Find the standard deviation of this normal distribution.
Answer
Using the quartiles from the box plot, where Q1 is at 36 kg and Q3 is at 54 kg, we can calculate the interquartile range (IQR) as follows: ( IQR = Q3 - Q1 = 54 - 36 = 18 ). For a normal distribution, the standard deviation is approximately ( \sigma = \frac{IQR}{1.35} ). Thus, ( \sigma \approx \frac{18}{1.35} \approx 13.33 ). Therefore, the standard deviation of this normal distribution is approximately 13.33 kg.