Descriptive Statistics - Describing Variability of the Data
3 important questions on Descriptive Statistics - Describing Variability of the Data
What does the range of a variable describe?
It shows the spread of the data, so the difference between the largest and smallest observation.
What are the properties of the standard deviation and what is its formula?
A deviation of an observation yi from the sample mean ȳ is (yi - ȳ), the difference between them.
By taking the square root of
, you will receive the standard deviation, if not it will be the variance. The smaller the standard deviation, the less variable a sample is. The standard deviation is never negative and only 0 if all observations have the same value. The standard deviation can be affected by an outlier.
By taking the square root of
, you will receive the standard deviation, if not it will be the variance. The smaller the standard deviation, the less variable a sample is. The standard deviation is never negative and only 0 if all observations have the same value. The standard deviation can be affected by an outlier.
What is the Empirical Rule?
If the histogram of the data is approximately bell-shaped, then:
- About 68% of the observations fall between ȳ - s and ȳ + s.
- About 95% of the observations fall between ȳ - 2s and ȳ + 2s.
- All or nearly all observations fall between ȳ - 3s and ȳ + 3s.
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