Summary Measures

Summary Measures

Understanding Summary Measures

• Summary measures or summary statistics provide simplified and condensed representations of collected data.
• They allow for easier interpretation and analysis by summarising large quantities of data into few numbers.

Central Tendency

• Measures of central tendency give a ‘typical’ or ‘central’ value in your data.
• The mean is the arithmetic average of a data set. It is calculated by adding all numbers in the set and dividing by the count of numbers.
• The median is the middle value in the sorted data set. If the count of numbers is odd, the median is the middle number. If its even, the median is the average of the two middle numbers.
• The mode is the most frequently occurring value in the data set. A data set can have more than one mode.

Dispersion

• Measures of dispersion indicate how spread out data points are from each other.
• The range is the difference between the highest and the lowest values in the dataset.
• The interquartile range is the range of the middle 50% of the data, it is calculated by subtracting the first quartile from the third quartile.
• The variance measures the average distance that each point in the dataset is from the mean. Higher variance means more spread out data.
• The standard deviation is the square root of the variance. It is preferred over the variance because it is in the same units as the data.

Skewness and Kurtosis

• Skewness measures how lopsided a distribution is. It indicates the extent and direction of skew (departure from horizontal symmetry).
• Positive skewness means the tail on the right side is longer or fatter than the left side. Negative skewness is just the opposite.
• Kurtosis measures the ‘tailedness’ of the distribution. It shows whether the data are heavy-tailed or light-tailed compared to a normal distribution.

Using Summary Measures

• Always consider the context of data when interpreting summary measures.
• Beware of outliers, as they can significantly influence the mean and standard deviation.
• Carefully analyse results in terms of the subject matter and check whether they make sense logically and practically.
• Remember that these measures alone do not provide a full understanding of the data. Always combine them with sound graphical presentations such as histograms, box plots etc. for a more comprehensive analysis.