Deviations of Data Set

single_deviation(actual, mean)

Calculates the difference between the actual value from a data set and the mean of that data set

Parameters

  • actual (int or float) – Value actually provided by an initial data set

  • mean (int or float) – Average value of the data set

Raises

TypeError – Arguments must be integers or floats

Returns

deviation – Difference between the actual value and the mean of the data set

Return type

float

See also

mean_value(), single_residual(), correlation_coefficient()

Notes

  • Observed value: \(y\)

  • Mean of all observed values: \(\bar{y}\)

  • Deviation: \(d = y - \bar{y}\)

  • Deviation

Examples

Import single_deviation function from regressions library
>>> from regressions.statistics.deviations import single_deviation
Determine the deviation for an actual value of 7.8 and a mean of 13.75
>>> deviation_small = single_deviation(7.8, 13.75)
>>> print(deviation_small)
-5.95
Determine the deviation between an actual value of 6.1 and an mean of -19.7
>>> deviation_large = single_deviation(6.1, -19.7)
>>> print(deviation_large)
25.799999999999997
multiple_deviations(actual_array)

Generates a list of the differences between the actual values from an original list and mean value of the actual values from that original list

Parameters

actual_array (list of int or float) – List containing the actual values observed from a data set

Raises

  • TypeError – Arguments must be 1-dimensional lists

  • TypeError – Elements of arguments must be integers or floats

Returns

deviations – List of differences between the actual values and the mean value for all elements from the original list

Return type

list of float

See also

mean_value(), multiple_residuals(), correlation_coefficient()

Notes

  • Observed values: \(y_i = \{ y_1, y_2, \cdots, y_n \}\)

  • Mean of all observed values: \(\bar{y} = \frac{1}{n}\cdot{\sum\limits_{i=1}^n y_i}\)

  • Deviations: \(d_i = \{ y_1 - \bar{y}, y_2 - \bar{y}, \cdots, y_n - \bar{y} \}\)

  • Deviation

Examples

Import multiple_deviations function from regressions library
>>> from regressions.statistics.deviations import multiple_deviations
Generate a list of deviations from this data set [8.2, 9.41, 1.23, 34.7]
>>> deviations_short = multiple_deviations([8.2, 9.41, 1.23, 34.7])
>>> print(deviations_short)
[-5.185000000000002, -3.9750000000000014, -12.155000000000001, 21.315]
Generate a list of deviations from this data set [5.21, 8.2, 9.41, 1.23, 10.52, 21.76, 34.7]
>>> deviations_long = multiple_deviations([5.21, 8.2, 9.41, 1.23, 10.52, 21.76, 34.7])
>>> print(deviations_long)
[-7.7942857142857145, -4.804285714285715, -3.5942857142857143, -11.774285714285714, -2.484285714285715, 8.755714285714287, 21.69571428571429]