Module 5 - Variability

# Module 5 - Variability - Module 5 Variability A Frequency...

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Module 5 – Variability A. Frequency distributions 2 primary components we are concerned about when describing our data: central tendency and variability (spread)

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Mean (Average) The mean is the measure of central tendency used for ratio-interval scale data Population mean = µ Sample mean = 𝑋𝑋 We use the statistic 𝑋𝑋 to estimate the population parameter µ REVIEW: FROM MODULE 1
Module 5 – Variability A. Frequency distributions Fish Length (cm) 5.9 10.2 7.6 13.8 6.9 13.9 8.9 9.4 10.3 6.8 5.9 10.3 8.6 5.9 9.1 6.3 5.9 8.3 4.1 5.2 Measure 20 yellow tang, create a histogram to show the frequency distribution of the lengths

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Module 5 – Variability A. Frequency distributions Pair/share: Which frequency distribution has a higher central tendency and which has higher variability? A B Fish Length (cm) Fish Length (cm)
Module 5 – Variability A. Frequency distributions B. Probability Density Curves Fish Length (cm) Fish Length (cm)

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Module 5 – Variability B. Probability Density Curves C. Frequency distributions are useful for determining the probability of obtaining certain values Values of 75 or greater (shaded) occur only about 5% of the time. Probability of getting a value of 75 or greater is about 0.05 Values of 75 or greater (shaded) occur about 1/3 of the time. Probability of getting a value of 75 or greater is about 0.33
Variance = Sum of squares n-1 Standard Deviation = Variance Coefficient of Variation = Standard Deviation Mean units 2 units B. Measures of dispersion (variability or spread ) 1. Sum of squares 2. Variance 3. Standard Deviation 4. Coefficient of Variation

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B. Measures of dispersion (variability) 1. Sum of squares Standard formula: Fish Length (cm) 5.9 10.2 7.6 13.8 6.9 13.9 8.9 9.4 10.3 6.8 5.9 10.3 8.6 5.9 9.1 6.3 5.9 8.3 4.1 5.2 = 134.2 cm 2 cm
B. Measures of dispersion (variability) 1. Sum of squares But to calculate it faster you can use the “machine formula”: Pair/Share: Say in words what this formula means… means that you sum all the data, then square the sum means that you square all the data, then sum the squared values

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