# Chapter 4 - Variability .docx - Chapter 4 1 Variability...

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Chapter 4 Variability: Chapter 4 Learning Objectives 1. Students should understand the general purpose for measuring variability and they should be able to recognize the difference between scores with high variability versus scores with low variability. 2. Students should be able to define and calculate the range, but they should also realize that this is a relatively crude measure of variability. 3. Students should understand the concept of standard deviation as a measure of the standard distance from the mean. 4. Students should be able to calculate SS (sum of squared deviations), variance, and standard deviation for a sample and for a population. Tools You will Need 1. Summation notation (Chapter 1) 2. Central tendency (Chapter 3) – mean and median Read “Preview” (p. 100) Remember, to say that things VARY is to say they are not all the same. If I ask you how many hours you study per week for this class, each of you would provide me different answers. Some of you may say 5 hours, and others may say ½ hours. If the scores in a distribution are the same or close to one another, we say the variability is small. If the scores in a distribution are different or far away from one another (quantitatively), we say the variability is large. Variability is a measure of the dispersion or spread of scores in a distribution It provides a numeric index of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together It ranges from 0 to + ∞ 1

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Chapter 4 A woman’s purse was stolen by a man at the bar. A police officer asked 10 witnesses (5 college students and 5 noncollege students) to estimate the age of the thief. Which group makes a more accurate estimation if the thief was actually a 25-year-old man? College students: 23, 24, 25, 26, 27; Noncollege students: 15, 20, 25, 30, 35 The college students, right? The mean estimated age is the same for both groups, but the variability in their responses among college students is much smaller, indicating precision of their estimation is better. As with central tendency, there are several ways to measure variability: Range, Variance, and Standard Deviation RANGE 1. Range calculation a. Range = highest value - lowest value (SPSS uses this formula) b. “Range” ranges from 0 to + ∞ i. Data: 1, 4, 5, 6, 8, 9, 13 Range = 13-1 = 12 Answer. Adult weight distribution (b) because weights are spread over a much wider range. Q. Between the distributions a and b , which one shows higher variability? The textbook provides two additional ways to obtain the range. Range = the upper real limit of the largest score – the lower real limit of the smallest score Range = (highest value - lowest value) + 1 Let’s use “highest value-lowest value” definition as it is the simplest 2
Chapter 4 ii. Data: -9, -7, 0, 1, 6 Range = 6-(-9) = 15 iii. Data: -100, -93, -80, -23, -11 Range = -11-(-100) = 89 c.

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