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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