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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 and counts workers as t... 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
Step 2
State and briefly describe an alternative method of non-random sampling Charlie could have used to obtain a sample of 40 workers.
Answer
An alternative method is quota sampling. Charlie could select a specific number of workers from different departments or groups, ensuring a range of perspectives. For instance, he might choose 10 workers from each of four departments every 10 minutes.
Step 3
Step 4
Step 5
Calculate the mean and the standard deviation for these data.
Answer
Using the formulas for the mean (ar{x}) and standard deviation ():
Mean: ar{x} = rac{ ext{total time}}{n} = rac{4133}{95} ext{ (approximately )} = 43.5 ext{ minutes}.
Standard Deviation: s = rac{ ext{sqrt}igg( rac{ ext{sum of squares}}{n - 1}igg) - ar{x}^2} ext{ (with values plugged in), it results in $s ext{ (approximately) } = 15.4 minutes.}
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.
Answer
Due to potential outliers and the skewness of the data, it is advisable to use the median and interquartile range (IQR) to describe the data. This method provides a more robust measure of central tendency and variability without being influenced by extreme values.
Step 7
Explain which two values Taruni must have changed and whether each of these values has increased or decreased.
Answer
Taruni must have changed the median and the upper quartile (Q3). Given that both Rana's and David's travel times decreased, it is likely that both the median and Q3 have decreased as more values close to or below these measures have been introduced.