Measures of Dispersion Flashcards
What is dispersion (variability) in statistics?
The variety, diversity, and amount of variation between scores in a dataset.
Key measures of dispersion:
Index of Qualitative Variation (IQV)
Range & Interquartile Range (IQR)
Variance & Standard Deviation
What is the IQV used for?
It measures the degree of variation in nominal variables.
What is the range of IQV?
0.00 (no variation) to 1.00 (maximum variation).
What are the steps to calculate IQV?
Create a frequency distribution.
Convert frequencies to percentages.
Square the percentages.
Sum the squared percentages.
Use the formula to calculate IQV.
What is the range?
The difference between the highest and lowest score.
R=HighestScore− LowestScore
What are the limitations of the range?
Only considers two scores.
Sensitive to outliers.
Provides no details about variation within the dataset.
What is the IQR?
The range of the middle 50% of scores, from Q1 to Q3.
Q=Q3−Q1
Why is IQR preferred over range?
It is not influenced by outliers.
What are the steps to calculate IQR?
Arrange data from lowest to highest.
Find the median (Q2).
Find Q1 (median of the lower half).
Find Q3 (median of the upper half).
Compute
Q
3
−
Q
1
Q3−Q1.
What do variance and standard deviation measure?
The average spread of data from the mean.
What is the difference between variance and standard deviation?
Variance (s^2 ) is the average of squared deviations.
Standard deviation (s) is the square root of variance.
What does dispersion tell us about the shape of the distribution?
More dispersion → Flatter curve
Less dispersion → Taller curve
How does standard deviation change with dispersion?
Small SD → Data is clustered near the mean.
Large SD → Data is spread out.
What factors determine which measure to use?
Level of Measurement (LoM)
Nominal → IQV
Ordinal → IQV, Range, IQR
Interval/Ratio → IQV, Range, IQR, Variance, Standard Deviation
Shape of Distribution
Symmetrical → Mean & SD are best
Skewed → Median & IQR are better
Research Objectives
