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

An alternative method could be quota sampling. For example, Charlie could decide to sample 10 workers from each department in the company, ensuring that he collects data from a variety of groups within the workforce.

Taruni used a census method by asking every member of the company for their travel time, ensuring she gathered data from the entire population.

To find the interquartile range (IQR), we calculate it as the difference between the upper quartile (Q3) and the lower quartile (Q1). Assuming the data summary and box plot indicate Q1 = 26 and Q3 = 40, the IQR can be calculated as follows:

$IQR = Q3 - Q1 = 40 - 26 = 14$

The mean (ar{x}) can be calculated as follows:

ar{x} = \frac{\Sigma x}{n} = \frac{4133}{95} \approx 43.5

For the standard deviation ($ext{s.d.}$), we use the formula:

$s.d. = \sqrt{\frac{\Sigma x^2}{n} - \left(\frac{\Sigma x}{n}\right)^2}$

From the data, we calculate:

$\text{s.d.} = \sqrt{\frac{202294}{95} - (43.5)^2} \approx 15.4$

Given the presence of outliers in the data, it is recommended to use the median and interquartile range (IQR) rather than the mean and standard deviation. Outliers can skew the mean and inflate the standard deviation, making them less representative of the central tendency and spread of the data.

The two values that Taruni must have changed are the mean and the standard deviation. The mean has likely decreased due to Rana's and David's reduced travel times, and the standard deviation would also decrease because the overall spread of the data would reduce with these lower values in the dataset.