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It’s the summary of the textbook on Analytical Techniques 1A
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- University Of Johannesburg (UJ)
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LEARNING UNIT 3: Numeric Descriptive StatisticsLearning objectives
• Distinguish between measures of central location, non-central location,
dispersion and skewness
• Compute and interpret the mode, median, arithmetic mean, weighted mean
and geometric mean
• Compute and interpret percentiles
• Compute and interpret the range, inter-quartile range, variance, standard
deviation and coefficient of variation
Textbook reference
Chapter 3: §3.1 – §3.5, Exclude §3.6 – §3.10
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,INTRODUCTION
Descriptive statistics are numerical summary measures used to describe the data
collected from a sample in terms of location, dispersion and skewness. These
measures are used in most statistical analyses.
MEASURES OF CENTRAL LOCATION
A measure of central location (or tendency) is a single value that summarises the
centre of a distribution. The commonly used measures of central location are
mode, median and mean.
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, Mode
For raw data and ungrouped frequency data the mode is the value of the variable
that occurs most frequently. A variable can have one, two, more than two, or no
mode. For grouped frequency data it is not possible identify the value occurring
most frequently since the data were grouped into class intervals and information
were lost. For such data formats the class with the highest frequency is the modal
class and the mode can be estimated using the midpoint of the modal class.
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