3VL Measures of dispersion: Flashcards
1 quartile
viertel 1/4 quarter
1 quintile
1/5 one fifth
1 decentile
1/10 one ten
1 percentile
1/100 one over one hundred
Name Measures of Dispersion
- Range
- Interquartile range (IQR)
- Standard Deviation and variance
What does Range show?
The Range is simplest way of showing the variability
Formula of Range
Max-min
What are disadvantages of Range?
The range does not take into account
the data structure
Formula of IQR
Q3-Q1
What is IQR compering with range?
Range only distance between min and max but IQR is distance of the middle 50% of your observations
What does IQR represents?
IQR is representative of the central grouping of the data set
Advantage of IQR
Not affected by extreme values
How to find IQR?
- Find median (Q2)
- Exclude the mean
- Find mean with remaining values on
both sides from first mean (find Q1 and Q3) - Q3-Q1=IQR
What is Standard Deviation?
mean of all squared deviations in the dataset
What is deviation?
amount by which a value differs from the mean
Describe steps for calculating Standard Deviation
- Find the mean
- Find the distance of each value from the mean
- Square the deviations
- Sum up all squared deviations
- Divide by N
- Take the square root of the result
Formula of Standard Deviation
Check notes
How to interpretate Standard Deviation?
On average a value deviates by (SD) from the mean.
Change SD by calculated number
Symbol of Standard deviation
SD or S
When to write higher and lower SD?
lower SD stands for less variability
formula of variance
Squared standard Deviation or all steps of Standard deviation without last one
When is it possible to compare standard deviations from different datasets?
2 constraints when it is possible:
1. If the datasets have the same unit of measurement (both = Euros)
AND
2. If there are the same number of observations (N/n) in the two datasets
How to understand if variation is high in different datasets?
To understand whether variation is high in different datasets, one can compare it to the mean use Coefficient of variation (CV)
Formula of CV (Coefficient of variation)
Check notes
With what level data can CV be used?
CV can only be used for ratio level data and should not be used for interval level data
What rule of thumb does CV have?
CV>1 rather high variability
CV<1 rather low variability
