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 stratified sampling, where the population is divided into distinct subgroups (strata) based on specific characteristics, such as department or job role. Charlie could select a proportional number of workers from each subgroup to ensure representation in the sample.

Taruni used a census approach to data selection, where she collected the travel time data from every member of the company instead of a sample.

The interquartile range (IQR) can be calculated as follows:

$IQR = Q3 - Q1 = 58 - 26 = 32$

Thus, the interquartile range is 32 minutes.

To calculate the mean (ar{x}):

ar{x} = rac{ extstyle oldsymbol{ extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle}{95} = 43.5

To calculate the standard deviation ($ext{sd}$):

ext{sd} = rac{ ext{sqrt}(202294 - ar{x}^2)}{n} = rac{ ext{sqrt}(202294 - (43.5)^2)}{95} ext{ which results in } ext{approx } 15.4

Due to the presence of outliers in the data, which can skew the results, it is advisable to use the median and interquartile range (IQR) rather than the mean and standard deviation. The median and IQR are more robust measures that are less influenced by extreme values.

Taruni must have changed the maximum value and the minimum value in her box plot. The maximum value decreased from 140 minutes to the new value of 135 minutes (as David’s journey changed), and the minimum value decreased from 10 minutes to the new value of 35 minutes (as Rana’s journey changed). Thus, both values have decreased.