PH 167_Park_Module 4-1_Clean

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San Jose State University *

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Oct 30, 2023

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Summary Statistics & Probability Concepts PH 167 Biostatistics
Outline 1. Central Location: Mean, Median, Mode 2. Comparison of the Mean, Median, and Mode 3. Spread: Range, Quartiles, Five-Point Summary, Interquartile Range 4. Frequency table 5. Boxplots 6. Boxplots – Tukey’s hinge method 7. Spread: Variance and Standard Deviation 8. What is Probability?
§ Mean: the arithmetic average of a data set (the most common measure of central location) § 21, 42, 5, 11, 30, 50, 28, 27, 24, 52 § n = ? § ∑ !"# $ ࠵? ࠵? § ̅࠵? = # $ ∑ ࠵? ࠵? Central Location: Mean 3
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§ Gravitational center: Central Location: Mean (Cont’d) 4
§ Susceptibility to outliers and skews: Central Location: Mean (Cont’d) 5
§ The mean from a frequency table: ̅࠵? = ∑ ࠵? ࠵? ࠵? ࠵? Central Location: Mean (Cont’d) 6
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§ Median: the midpoint of a distribution. § The median is relatively resistant to outliers and skew. Central Location: Median 7
8
§ Mode: the most frequently occurring value in the data set. Central Location: Mode 9
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10
Comparison of the Mean, Median, and Mode 11
Spread: Range, Quartiles, Five-Point Summary, Interquartile Range § Range = maximum – minimum § Quartiles: dividing the data set into four equal segments o Q0: minimum o Q1: lower hinge o Q2: median o Q3: upper hinge o Q4: maximum § Interquartile range (IQR) = Q3 – Q1 12
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Spread: Range, Quartiles, Five-Point Summary, Interquartile Range (Cont’d) 13
Frequency Table
Boxplots – Tukey’s hinge method 15 § Tukey’s hinge method: When n is odd, the median is included in both the lower half and upper half of the data when determining the locations of Q1 and Q3.
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Boxplots 16 § Site 1: 22, 24, 28, 32, 36, 38, 42, 68 § Site 2: 32, 33, 34, 36, 36, 38, 39, 40
17
Spread: Variance 18
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Spread: Standard Deviation 19
What is Probability? 20 § Relative frequency of an event. § The mean from a frequency table: ̅࠵? = ∑ ࠵? ࠵? ࠵? ࠵?
21
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