Unit 4 Summarising Data: Measures of Central Tendency and Dispersion Overview In Unit 3, we examined a few formats for presenting data. In this context, we said that tables and charts are valuable because they can give us a quick impression of the general characteristics of the data. We have also mentioned that tables and charts are inherently limited in terms of presenting the data. However, there are a few mathematical procedures, which, when used alongside the tables and charts, will help us get a better understanding of the data. In this unit, we will be discussing two of these mathematical procedures: central tendency (the central values about which the data appear to be spread, such as the mean, the median and the mode) and the variability or dispersion of the data. We will discuss a few other mathematical procedures in Units 6, 7 and 8. Unit 4 Learning Objectives After completing this unit, you should be able to: • discuss the mean, median and mode as measures of central tendency in statistics; • calculate the mean, median, and mode of a given data set; • describe the relationship among the measures of central tendency; • explain the concept of ‘skewness’ in statistics; • discuss the standard deviation and variance as measures of dispersion in statistics; • determine the semi-interquartile range of a given set of data; • determine standard deviation (SD) and variance from a set of data. The sessions in this Unit are: Session 1: Measures of central tendency. Session 2: Measures of dispersion. Session 3: Deriving measures from grouped data. 69
Note to students This unit contains several activities and one practice assignment at the end of the unit. You are to work on the activities on your own. If you have any questions or concerns please post a message in the unit discussion forum so that your E-tutor can provide assistance to you. The assignment is to be uploaded in the practice assignment area. 70
Session 1 Measures of Central Tendency Introduction A…