13F – skewness

What is ‘skewness’? Skewness is an additional tool to help us analyse and compare sets of data There are four different types of ‘skewness’: Symmetrical: data equally distributed around the mean median and mean will both be the middle score. Positively Skewed: majority of the data at the lower end (tail = positive) Negatively Skewed: majority of the data at the upper end (tail = negative) Bimodal: data has two modes (peaks)

Worked example Is the graph symmetrical? Yes b) What is the mode? Mode = number(s) with highest frequency Mode = 17 and 19 c) Can the mean and median be seen from the graph and, if so, what are their values? Since the graph is symmetrical, the mean and median are the same, so from this we can see that the middle score is 18 (which is both the mean and median in this case)

Worked example a) What is the modal class? The modal class is the class interval with the highest frequency Modal class = 81-90 b) Describe the skewness of the data set. Is it symmetrical, positively skewed, negatively skewed, or bimodal? The bulk of the data is at the higher end with the tail at the lower end, which means it is negatively skewed.

Questions to do: Exercise 13F page 461 questions 1, 2, 3, 4, 6, 7