WJEC Maths for AS: Applied sample

21 2.1 Interpreting diagrams for single variable data To complete the histogram, the frequency density needs to be calculated for the missing bars using the data in the table. We use the formula frequency density = frequency class width For class boundary 50 < x ≤ 60, frequency density = frequency class width = 25 10 = 2.5 For class boundary 60 < x ≤ 80, frequency density = frequency class width = 10 20 = 0.5 For class boundary 85 < x ≤ 100, frequency density = frequency class width = 30 15 = 2 The bars can now be added to the histogram. 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0 0 10 20 30 40 50 60 70 80 90 100 Mark (%) Frequency density Box and whisker diagrams A box and whisker diagram is a diagram that gives a visual representation to the distribution of data. The diagram highlights where most of the values lie and any values that greatly differ from the norm which are referred to as outliers . 50 55 60 65 70 75 80 85 90 95 100 Highest mark Lower quartile Median Upper quartile mark mark mark Lowest mark Student marks in a maths test The left-hand side of the box represents the lower quartile and the right-hand side represents the upper quartile. The vertical line inside the box represents the median. The length of the side of the box represents the inter-quartile range. The quartiles cut the data into four equal sections when the data is arranged in order of size. The ϐirst cut is the lower quartile (LQ or Q 1 ), the second cut is the median and the third cut is the upper quartile (UQ or Q 3 ). The difference between the upper and lower quartiles is called the interquartile range (IQR). So IQR = UQ − LQ or IQR = Q 3 − Q 1