Charlie is studying the time it takes members of his company to travel to the office - Edexcel - A-Level Maths Mechanics - Question 4 - 2018 - Paper 1
Question 4
Charlie is studying the time it takes members of his company to travel to the office. He stands by the door to the office from 08:40 to 08:50 one morning and asks wo... show full transcript
Worked Solution & Example Answer:Charlie is studying the time it takes members of his company to travel to the office - Edexcel - A-Level Maths Mechanics - Question 4 - 2018 - Paper 1
Step 1
State the sampling method Charlie used.
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Answer
The sampling method used by Charlie is convenience sampling, as he is asking people who happen to arrive at the office during a specific time frame.
Step 2
State and briefly describe an alternative method of non-random sampling Charlie could have used to obtain a sample of 40 workers.
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An alternative method Charlie could use is quota sampling. In this method, Charlie could aim to ask an equal number of workers from different departments or job roles over the same time period, ensuring representation across various groups within the company.
Step 3
State the data selection process Taruni used.
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Taruni used a census method by asking every member of the company about their travel time to gather complete data on the entire workforce.
Step 4
Write down the interquartile range for these data.
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The interquartile range (IQR) can be calculated as: IQR = Q3 - Q1, where Q1 is the lower quartile and Q3 is the upper quartile. The exact values can be extracted from the box plot.
Step 5
Calculate the mean and the standard deviation for these data.
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State, giving a reason, whether you would recommend using the mean and standard deviation or the median and interquartile range to describe these data.
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It would be advisable to use the median and interquartile range due to the presence of outliers, which can skew the mean and inflate the standard deviation.
Step 7
Explain which two values Taruni must have changed and whether each of these values has increased or decreased.
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The two values Taruni must have changed are the mean and the standard deviation. After Rana's journey decreased significantly and David's journey also reduced, it is likely that both the mean and standard deviation have decreased, as these two values will adjust towards the new lower travel times.
