C2 - Measures of Location and Spread

• A measure of location is a single value which describes a position in a data set. If the single value describes the centre of the data, it is called a measure of central tendency.
• The mode or modal class is the value or class that occurs most often.
• The median is the middle value when the data values are put in order.
• To find the lower quartile for discrete data, divide n by 4. If this is a whole number, the lower quartile is halfway between this data point and the one above. If it is not a whole number, round up and pick this data point.
• To find the upper quartile for discrete data, find 3/4 of n. If this is a whole number, the upper quartile is halfway between this data point and the one above. If it is not a whole number, round up and pick this data point.
• When data is presented in a grouped frequency table you can use a technique called interpolation to estimate the median, quartiles and percentiles. When you use interpolation, you are assuming that the data values are evenly distributed within each class.
• The range is the difference between the largest and smallest values in the data set.
• The interquartile range (IQR) is the difference between the upper quartile and the lower quartile, Q3-Q1.
• The interpercentile range is the difference between the values for two given percentiles.
• Coding is a way of simplifying statistical distributions. Each data value is coded to make a new set of data values which are easier to work with.