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 that Charlie could have used is quota sampling. This method involves selecting specific groups to ensure that the sample reflects certain characteristics, such as different departments or job roles. Charlie could approach a predetermined number of workers from each group until a total of 40 is reached.

Taruni used a systematic sampling method by asking every member of the company for their travel time to the office, ensuring that every individual was given an equal opportunity to provide their data.

The interquartile range (IQR) can be calculated as follows: IQR = Q3 - Q1. From the box plot, Q1 is at 26 minutes and Q3 is at 58 minutes, therefore:

$ext{IQR} = 58 - 26 = 32 ext{ minutes}$

To find the mean (μ):

ar{x} = \frac{\sum x_i}{n} = \frac{4133}{95} \approx 43.5 \text{ minutes}

To calculate the standard deviation (σ):

$\sigma = \sqrt{\frac{\sum x^2}{n} - \mu^2} = \sqrt{\frac{202294}{95} - (43.5)^2} \approx 15.4 \text{ minutes}$

I would recommend using the median and interquartile range (IQR) because there are outliers in the data. The presence of outliers can skew the mean and inflate the standard deviation, making them less representative of the typical journey times.

Taruni must have changed the maximum journey time from 75 minutes to 35 minutes, and the second high value from 60 minutes to 33 minutes. Both values have decreased.