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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 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 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 2
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
Charlie could have used quota sampling. In this method, he would set specific quotas for various categories of workers (e.g., by department or role) to ensure diversity in the sample until he reaches the target of 40 workers.
Step 3
Step 4
Step 5
Calculate the mean and the standard deviation for these data.
Answer
To calculate the mean, use the formula: ext{Mean} = rac{ ext{Sum of all journey times}}{n} = rac{4133}{95} ext{ minutes} \\ \text{The standard deviation can be calculated using the formula:} \\ ext{Standard Deviation} = ext{sqrt} \left( \frac{\sum x^2}{n} - \text{Mean}^2 \right)
Step 6
State, giving a reason, whether you would recommend using the mean and standard deviation or the median and interquartile range to describe these data.
Answer
I would recommend using the median and interquartile range. The presence of outliers can skew the mean and standard deviation, making these measures less representative of the central tendency and spread of the data.
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 mean and standard deviation. With Rana's journey decreasing from 75 minutes to 35 minutes, the mean is likely to decrease. Similarly, with David's journey decreasing from 60 minutes to 33 minutes, the spread of the data may also decrease, likely affecting the standard deviation.