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PEDS109 (14)
John Dunn (14)
Lecture

Oct 12 - variability.doc

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Department
Physical Education and Sport
Course
PEDS109
Professor
John Dunn
Semester
Fall

Description
Oct 12 – Variability Variability is how much the scores vary in a data set • Definition – variability provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are apread out or clustered together (p 104) • Related to homogeneity vs. Heterogeneity • Ex of a homogenous data set – taking the top 100 golfers in teh world and looking at their typical scores on a golf course. They would relatively close together. • Ex. Heterogeneity data set – if we randomly selected 100 golfers of various skill levels and compared scores, the scores would be widely spread out. There is more variation in abilities and variations of scores. • Homogenous data sets are bad for finding correlational studies Once we get a greater spread of scores, the underlying relationship between variables will come to light Range • Range is the distance between the largest score (Xmax) and lowest score (Xmin) in a distribution • This means the range and variation of the scores is calculated by 2 data points • Its risky because all sort of things can happen between these 2 scores, then we are distorting the distributional characteristics • Ex. 30.5 is Xman and 22.5 is Xmin. So 30.5 – 22.5 = 8 • Even though the range is 8 we would likely put 22.5 – 30.5 • If ever asked to compute range, don't use upper and lower real limits! Ex. Normal curve: 1,2,3,4,5,5,6,6,7,7,8,9,10 normal curve Greatly influenced by extreme scores: 1,2,3,4,5,6,6,6,7,7,8,9,25 (range = 24) Interquartile & Semi- Interquartile Range Detection of outliers = 1.5 x IQR beyond Q1 and Q3 To detect ourliers, IQR stand for interquartile range We calculate the IQR iQR is the difference between a score at the 3 quartile and the 1 quartilest the value we get, we multiply it by 1.5 ex. If q3 was 15 and q1 was 5, we would go 15-5 = 10 so our IQR is 10 we then multiply 10 by 1.5 and we get 15 then we say outliers would be scores that are 15 + 15 (the Q3score)= 30 so any score over 30 is an outlier on the other hand, we would go 5-15 = -10 so any score less than -10 is an outlier IQR is the range of scores that cover the middle 50% of our data So we get a better sense of our data but it doesn tell us what is going on below Q1 and Q3 To compute q1, we go: I = 25/100 x n Q3: I = 75/100 x n 1 quartile: score corresponding to 25 percentile nd th 2 quar
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