Measures of Central Tendency Computation Flashcards
The Arithmetic Mean is the
sum of observations divided by the number of observations.
Arithmetic mean is often used as
a measure of the typical outcome for an asset.
The Sample Mean is
an arithmetic average computed for a sample.
The Sample Mean is calculated as
(X bar) = Summation of all samples / number of samples
The Median is
the value of the middle item in the set of items that has been sorted into ascending or descending order (i.e. the 50% percentile)
In an odd-numbered sample of n items, the median is the value of the item that occupies the
(n + 1)/2 position
If a sample has an even number of observations…
the median is the mean of the two values in the middle.
The Mode is
the most frequently occurring value in a distribution.
The distribution can have no modes or even several modes in which case it can be called:
Unimodal
Bimodal
Trimodal
The mode is the only measure of central tendency that can be used with
nominal data.
The Weighted Mean allows for
different weights for different observations.
The Weighted Mean is calculated as:
Xw = Sum of (number x weighting factor) / sum of all the Weights
Where the sum of weights always equals to 1.
The Geometric Mean - frequently used to average..
rate of change over time to compute the growth rate of a variable.
The Geometric Mean formula is:
x̄g = n√x1*x2…xn
**The geometric mean exists only if the product under the square root sign is non-negative!
If the values for the Geometric Mean are negative:
we need to convert the variables into decimal, then add 1, and after you multiply each of the variables and take an nth root of the product you have to subtract 1
