WJEC Maths for AS: Applied sample

2 Data presentation and interpretation 26 0.25 0.20 0.15 0.10 0.05 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 x Probability This graph is no longer symmetrical. It is positively skewed which means the bulk of the probability falls in the smaller numbers 0, 1, 2, … , and the distribution tails off to the right. 0.25 0.20 0.15 0.10 0.05 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 x Probability The above graph is negatively skewed as the bulk of the probability falls into the higher numbers and the probability tails off to the left. Here are some graphs which show the overall shape of the various measures of skew. Negatively skewed Normal (no skew) Positively skewed Negative direction Positive direction The normal curve represents a perfectly symmetrical distribution This distribution is positively skewed as it tails off in the direction of higher values for X . This distribution is negatively skewed as it tails off in the direction of lower values for X . To help remember which way graphs are skewed. You go by the direction of the tail – if it is towards larger values of X it is positively skewed and if it is towards smaller values of X it is negatively skewed. BOOST Grade ⇪⇪⇪⇪ If the median is to the left of the mean, it means the distribution is positively skewed. If the median is to the right of the median it means the distribution is negatively skewed.