Central Tendency And Dispersion Flashcards
Measures of Central Tendency identify
the Center, or average, of a dataset. It can be used to represent the typical, or expected, value in the dataset.
the Arithmetic Mean is the
Sum of the Observation values divided by the number of observations. It is the most widely used measure of central tendency
An example of an Arithmetic Mean is a Sample Mean, which is
The sum of all the values in a sample of a population (€x) divided by the number of observations in the sample, n
the Sample Mean is used to
make inferences about the population mean
The median is the
Midpoint of a dataset, where the data are arranged in ascending or descending order
The Median is important because
the Arithmetic Mean can be affected by outliers, which are extremely large or small values. When this occurs the Median is a better measure of Central Tendency than the Mean
the Mode is
the value that occurs most frequently in a dataset
a Trimmed Mean excludes
a stated percentage of the most extreme observations
A 1% trimmed mean, for example, would discard
The lowest 0.5% and the highest 0.5% of the observations
In using a Winsorized Mean, instead of discarding the highest and the lowest observations, we
substitute a value for them
Quantile is the general term for
a value at or below which a stated proportion of the data in a distribution lies
Examples of Quantiles are
Quartile - distribution is divided into quarters
Quintile - distribution is divided into fifths
Decile - distribution is divided into tenths
Percentile - distribution is divided by hundredths
The difference between the third quartile and the first quartile is known as
the Interquartile Range
The difference between the third quartile and the first quartile is known as
the Interquartile Range
In a Box and Whisker Plot, the box represents
the central portion of the data, such as the interquartile range
In a Box and Whisker Plot, the vertical line represents
the entire range of observations
Dispersion is defined as
the variability around the Central Tendency identify
the Range is a relatively simple measure of
Variability
the Mean Absolute Deviation (MAD) is the average of the
absolute values of the deviations of individual observations from the Arithmetic Mean
the Sample Variance, s^2, is the measure of
dispersion that applies when we are evaluating a sample of n observations from a population
the Sample Standard Deviation is the
Square root of the Sample Variance
The Sample Standard Deviation can be interpreted as
an Unbiased Estimator of the Population Standard Deviation
Relative Dispersion is the
amount of variability in a distribution around a reference point or benchmark
Relative Dispersion is commonly measured with the
Coefficient of Variation (CV) which is:
Standard Deviation of x
__________________________
Average value of x
