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

Charlie could have used systematic sampling. In this method, he could select every nth worker arriving at the office during the observation period until he obtains a sample of 40 workers.

Taruni used a complete enumeration method, where she asked every member of the company to report the time taken for their journey to the office.

The interquartile range (IQR) can be calculated as the difference between the third quartile (Q3) and the first quartile (Q1) values. Assuming Q3 = 70 and Q1 = 30, the IQR is calculated as follows:

$IQR = Q3 - Q1 = 70 - 30 = 40$

The mean can be calculated using the formula:

ar{x} = rac{ ext{Sum of values}}{n} = rac{4133}{95} \approx 43.06

For the standard deviation (SD), use the formula:

$SD = ext{sqrt}\left( \frac{\sum (x_i - \bar{x})^2}{n - 1} \right)$

where $\sum (x_i^2) = 202294$. The steps involved include calculating the variance first, which can then be squared to find the standard deviation.

In this case, I would recommend using the median and interquartile range because the presence of outliers could significantly affect the mean and standard deviation, making them less representative of the dataset.

Taruni must have changed the maximum journey time and the minimum journey time based on the new information provided. The maximum journey time has decreased from 75 minutes to 35 minutes, indicating a reduction, while the minimum journey time has decreased from 60 minutes to 33 minutes, which also indicates a reduction.