Descriptive Statistics - Measure of Position
3 important questions on Descriptive Statistics - Measure of Position
What is the five-number summary of positions and how is it displayed in the box plot?
The five-number summary consists of:
The box of a box plot contains the central 50% of the distribution. The median is marked by a line in the box. The whiskers (lines extending from the box) extend to the maximum and minimum, except for outliers, which are marked separately.
- The minimum
- The lower quartile
- The median
- The upper quartile
- The maximum
The box of a box plot contains the central 50% of the distribution. The median is marked by a line in the box. The whiskers (lines extending from the box) extend to the maximum and minimum, except for outliers, which are marked separately.
When is an observation rated as an outlier?
An observation is an outlier if it falls more than 1.5 interquartile range above the upper quartile or more than 1.5 interquartile range below the lower quartile. It is best to rate it as a potential outlier.
Formula: Upper/lower quartile ± 1.5 * (IQR)
How do you calculate the z-score and what do you use it for?
The z-score is the number of standard deviations that an observation falls from the mean.
By the Empirical Rule, for a bell-shaped distribution it is very unusual for an observation to fall more than 3 standard deviations from the mean. So if an observation has a z-score larger than 3, it can be valued as an outlier.
By the Empirical Rule, for a bell-shaped distribution it is very unusual for an observation to fall more than 3 standard deviations from the mean. So if an observation has a z-score larger than 3, it can be valued as an outlier.
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