# AS91267 Exam Question

Can someone pls tell me some possible bullet points for shape, centre, spread with numerical evidence. Cheers

I must admit, Suzanne is a very peculiar woman, imagine Mum waiting in the bathroom with the clock and later creating graphs about all of that.

Anyway, to the topic. First, you can use your graphic calculator to find the summary statistics for this graph. (See guide at Level 2 Probability External 2020 Worked Solutions AS91267 - YouTube) Then you can make comments:

• Centre: mean time spent in the shower is 9.16min which is 1.16min greater than the mean of the normal distribution.

• Shape: in Suzanne’s results the mode is equal to 7min, which is one minute less than the median time (8min) and 2.16min less than the mean (9.16min). That signifies a right skew, rather than a normal distribution, in which mean, median and mode are equal. A skew is expected, as they can’t have a negative shower time but the upper limit can be as big as they want (or until Suzanne turns the hot water off).

• Spread: the range of the data from Suzanne’s survey is 20min (between just over 0 and 20 min) while 99.7% of data in the normal distribution would lie between 2 and 14 min, giving it a range of 12 min. The IQR of Suzanne’s data is 4min (between LQ = 7min and UQ = 11min) while for the suggested normal distribution IQR will be 2.7min - between LQ = 6.65min and UQ = 9.35min. That means there is more variety in the times Suzanne’s family can spend in the shower compared to the expected normal distribution model. (I used IQR as a measure of spread rather than standard deviation as standard deviation only applies to a normal distribution)

Overall, these results do not approach a normal distribution due to the right skew.