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Variability
quantifies how far apart values are from each other and from…
Variability
quantifies how far apart values are from each other and from the mean. It helps asses predictability, consistency, or diversity.
The Range
The range is first step in measuring variability.
It is an unreliable source of variability because it doesn’t include all scores in the range, just the extreme high and low.
It can also be defined as the number of measurement categories.
The Interquartile Range (IQR)
are the scores that make up the middle 50% of the distribution.
It divides the range into 4 parts.
It is the distance between the 25th (Q3) and 75th percentile (Q1), or between Q1 and Q3.
It is not influenced by extreme values.
Usually presented with the median in studies.
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A sample variability is biased in that it tends to underestimate a variability in a population.
To correct it we divide by n-1.
A sample statistic is unbiased if the average value of the statistic is equal to the population parameter.
Standard Deviation (SD)
is the square root of the variance. It's the most commonly used and the most important descriptive measure of variability!
SD measures the standard (or average) distance from the mean.
Sum of squares (SS) is the sum of the squared deviation scores. Except for minor changes in notation, the calculation of SS is identical for samples and populations.
Means & Medians
The standard deviation is usually with the mean in a study as a descriptive statistic of central tendency. It helps describe the amount of variability.
When the median is reported in the study, the interquartile range accompanies it.
In inferential statistics, the variability in the data influences how easy it is to see patterns.
As a rule, roughly 70% of the scores in a distribution are located within one standard deviation from the mean, and almost all of the scores (roughly 95%) are within two standard deviations of the mean
Sampling with replacement: A random sampling type where scores are replaced after every selection is made.