Data representation and interpretation

• The modal class is the value of the class which occurs most often, and can be used on both qualitative and quantitative data as long as values occur multiple times.
• The median is the middle value when the data values are put in order. It is used for quantitative data, particularly when there are extreme values.
• The mean is the sum of data values divided by the number of data values, and for data in a cumulative frequency table, it is the sum of the products of the data values and their frequencies, divided by the sum of frequencies.
• The mean is used for quantitative data and takes into account all values in the data, but is therefore also affected by extremes.
• The variance can be calculated by calculating the mean of the squares minus the square of the mean.
• Standard deviation is the square root of the variance.
• When y = (x - a)/b, the mean of y is (x' - a)/b where x' is the mean of x, and the standard deviation of y is x''/b, where x'' is the standard deviation of x.
• For a histogram, the area of each bar is the frequency multiplied by a constant, which will be different for each. The frequency density (height of the bar) is the frequency divided by the class width multiplied by the constant.
• When comparing data, comment on both a measure of location and a measure of spread, and use either the mean and standard deviation or median and interquartile range, but don't mix.