futurera | open data, time series, forecasting

SUMMARY

-statistics

The process of collecting and analyzing data to identify patterns and trends, remove bias and inform decision-making.

- Mean, median, mode are central values.
- MAD, Normal deviation measures the scatter.

The mean is the center of deviations. The mean is the aritmetic of deviations. It measures that value about wich 50 percent of the deviations are above and 50 percent of the deviations are below.

Calculation: Mean

X = ∑X_t / n = (27 + 23 + ... + 84) / 12 = 572 / 12 = 47.67

The median is the center of data. 50 percent of the values are above and 50 percent of the values are below.

Calculation: Median

An example.

We have values of 2, 4, 5, 6, 9, 11 and 12.

The median = 6
the values (2, 4 and 5) are below, and
the values (9, 11 and 12) are above.

Calculation: Mode

An example.

We have values of 1, 2, 5, 6, 6, 7, 10, 11.

The mode = 6

Calculation: MAD

An example.

We have values of 11 + 4 + 5 + 12 + 9 + 2 + 6
The mean is (11 + 4 + 5 + 12 + 9 + 2 + 6) / 7 = 7

The deviation is defined as X_t - (mean of X)
Sum of the deviations is:
(11-7) + (4-7) + ... + (6-7)
(4) + (-3) + (-2) + (5) + (2) + (-5) + (-1) = 0

the MAD is:
absolute(11-7) + absolute(4-7) + ... + absolute(6-7)
(4 + 3 + 2 + 5 + 2 + 5 + 1) = 17

The sum of the deviation of City Demand is -0.04. It should be 0, this is the result of rounding errors.

MAD for City Demand = absolute(-20.67) + absolute(-24.67) + ... + absolute(36.33) = 164.68

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

S = √( ∑(X - X)² / (n - 1) )

Where:
S = Sample Standard deviation
X = Actual value
X = Sample mean
n = Number of observations

Calculation: DEVIATION

The Mean of the example City Demand is 47.67

S = √(( -20.67² + -24.67² + ... + 36.33² ) / (12 - 1)) = 18.12