Exam (elaborations)
STA1501 Exam pack 2025(Descriptive Statistics and Probability)
- Institution
- University Of South Africa
STA1501 Exam pack 2025(Descriptive Statistics and Probability)
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STA1501 EXAM PACK2025
QUESTIONS AND
ANSWERS
FOR ASSISTANCE CONTACT
EMAIL:gabrielmusyoka940@gmail.com
, lOMoARcPSD|50013335
STA1501/1
Contents
ORIENTATION xiv
1 WHAT IS STATISTICS? 1
1.1 Learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.4 Parameter versus a statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.5 Types of variable and information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.5.1 Examples of Quantitative variable . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.5.2 Examples of Qualitative variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.6 Measurement scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.6.1 Nominal level of measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.6.2 Ordinal level of measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.6.3 Interval level of measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.7 Study Unit 1: Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
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2 GRAPHICAL DESCRIPTIVE TECHNIQUES 7
2.1 Learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Types of data and information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 Definitions of key terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.3 Classification of data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Describing set of nominal data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.3 Bar graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.5 Comparative bar graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.6 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.7 A pie chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.8 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Describing sets of interval data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.1 Frequency distribution for interval data . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.2 Graphs for interval data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.4 Shapes of histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Describing the relationship between two variables and describing time series data . . . . . . 17
2.5.1 Describing time series data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
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2.5.2 Describing the relationship between two interval variables . . . . . . . . . . . . . . 18
2.5.3 Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.6 Graphical excellence and graphical deception . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6.2 Graphical excellence and graphical deception . . . . . . . . . . . . . . . . . . . . . 20
2.7 Study Unit 2: Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 NUMERICAL DESCRIPTIVE TECHNIQUES 23
3.1 Learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Measures of central tendency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.1 The arithmetic mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.3 The median . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.5 The mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.6 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.7 Mean, Mode, Median: Choosing the best measure of central tendency . . . . . . . . 26
3.3 Measures of variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.1 The range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.2 The variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.3 The standard deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.4 The coefficient of variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
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