WJEC Maths for AS: Applied sample

25 2.1 Interpreting diagrams for single variable data The cumulative frequency curve can then be used to ϐind the median, lower quartile, upper quartile and percentiles (e.g. the range of 70% of electric cars). 200 180 160 140 120 100 80 60 40 20 0 0 50 100 150 200 250 Average distance travelled per charge (miles) Cumulative frequency Cumulative frequency graph showing miles per charge for electric cars × × × × × Upper quartile Lower quartile Median value Symmetric, positive and negative skew Graphs can be used to show probabilities. Here are the probabilities of obtaining certain values of the discrete variable X . 0.2 0.1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 x Probability The probability distribution is symmetrical about the two most probable values 7 and 8. The distribution is said to be symmetric. Half way through the cumulative frequency (i.e. half of 200 = 100) we draw a horizontal line to meet the curve and then produce it down vertically to read off the median value. We then use a similar method to read off the values at one quarter and three quarters of the cumulative frequency (i.e. at 50 and 150 respectively) to give the lower and upper quartiles. A graph of possible values for X, and the probabilities of obtaining them, is called a probability distribution. As the graph shows all the possible values X can take, the heights of all the bars will add up to one.