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 2
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 and records, as workers... 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 2
Step 1
State the sampling method Charlie used.
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Answer
Charlie used a convenience sampling method, as he gathered data from workers arriving at the office within 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 could be stratified sampling, where Charlie could select workers from different departments or shifts proportionately to ensure diverse representation. This could help in obtaining a more varied sample.
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 to report the time it takes them to travel to the office, ensuring data from all individuals was included.
Step 4
Write down the interquartile range for these data.
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The interquartile range (IQR) is calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1) of the data.
Step 5
Calculate the mean and the standard deviation for these data.
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To find the mean, use the formula Mean=n∑x=954133≈43.25.\nFor standard deviation, calculate the variance: Variance=n∑x2−(n∑x)2=95202294−(43.25)2.\nSolve this to find the standard deviation.
Step 6
State, giving a reason, whether you would recommend using the mean and standard deviation or the median and interquartile range to describe the data.
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I would recommend using the median and interquartile range (IQR) because the data may contain outliers, which can skew the mean and standard deviation, providing a misleading representation of central tendency and variability.
Step 7
Explain which two values Taruni must have changed and whether each of these values has increased or decreased.
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Taruni must have changed the maximum journey time and possibly the median journey time. The maximum would have decreased due to Rana's shorter journey, and the median could potentially decrease if a significant number of longer journeys were replaced by shorter ones.
