Charlie is studying the time it takes members of his company to travel to the office - Edexcel - A-Level Maths Statistics - Question 4 - 2018 - Paper 2

An alternative method is quota sampling. In this method, Charlie could define specific categories (e.g., age, department) and select a predetermined number of participants from each category until he reaches a total of 40 workers. This would ensure diversity in the sample without random selection.

Taruni chose to survey every member of the company, which is known as a census. This means she collected data from the entire population rather than a sample, ensuring comprehensive results.

The interquartile range (IQR) is calculated as follows: IQR = Q3 - Q1. Given the box plot information, this can be read off as 58 - 26 = 32 minutes.

The mean is calculated using the sum of the data (rac{4133}{95}) which results in approximately 43.5 minutes. The standard deviation is calculated using the formula: ext{s.d.} = rac{ ext{sum of squares} - ext{mean}^2}{n} = rac{202294}{95} - (43.5)^2 ext{, which is approximately } 15.4 ext{ minutes.}

I would recommend using the median and interquartile range (IQR) due to the presence of outliers in the data. The mean and standard deviation can be influenced heavily by extreme values, making them less representative of the central tendency and variability of the data in such cases.

Taruni changed the journey times for Rana and David. Rana's time decreased from 75 minutes to 35 minutes, indicating a significant reduction of 40 minutes. David's time decreased from 60 minutes to 33 minutes, indicating a decrease of 27 minutes. Both changes represent a reduction in journey times.