Variance
Variance reflects the average of the squares of the difference between each sample value and the mean of the population. Measures the degree to which a random variable or a set of data deviates from its expectation. The smaller the degree of deviation, the more stable the value of X. That is, the average of the distances away from the average, not the effective value (RMS). Calculated as follows:
Its mathematical meaning is:
Standard deviation
Standard deviation (Standard Deviation, STD), also known as the mean square deviation, is the arithmetic square root of the variance, represented by σ. Standard deviation can reflect the degree of dispersion of a data set. In fact, the variance and standard deviation both reflect the degree of dispersion of a data set, but the multiple change in the dimension caused by the square term in the variance cannot intuitively reflect the degree of deviation, so the standard deviation appears. Calculated as follows:
Mean Square
Deviation Mean Square Deviation (Standard Deviation): The mean square deviation is the standard deviation, and the standard deviation is the mean square deviation. The calculation formula is the same as the above formula:
Root mean square value (RMS)
Root mean square value (Root Mean Square, RMS): Also known as effective value, its calculation method is first square, then average, and then square root.
Calculated as follows:
Root Mean Square Error (RMSE)
Root Mean Square Error (Root Mean Square Error, RMSE): The square root of the ratio of the square of the deviation between the observed value and the true value to the number of observations N. The root mean square error is also represented by σ, which reflects the degree to which the measured data deviates from the true value. The smaller the σ, the higher the measurement accuracy.
Each X_obs in some data has a corresponding true value, so it can be compared with the true value. When the author once evaluated the accuracy of the ionospheric GIM grid product, it was different from each grid point in the official product, and the final result was RMSE.
Calculated as follows:
