Statistics​
Interpolation and extrapolation

Statistics

Univariate statistics

• Measures of middle (mean, median mode)
• Measures of spread (range and interquartile range)
• Measures of spread (standard deviation)
• Histograms
• Box plots​

Bivariate statistics

• Association between variables
• The effect of outliers on correlation
• Causality
• Interpreting Pearson's correlation coefficient
• Interpolation and extrapolation​​

When a scatterplot is created between two variables, we describe the highest and lowest x-variables as the upper and lower poles respectively. If a line of best fit has been drawn, then predictions can be made for one variable given the other.

• If we predict a value that occurs in between the lower and upper poles, then we say we are interpolating between the poles.
• If we predict a value that occurs outside of either the lower or upper pole, then we say we are extrapolating outside the poles.

The accuracy of the predictions in either situation depends on how strong the correlation of the original data was to begin with. However, the extrapolation of data assumes that the correlation is going to continue outside of the poles. The validity of this assumption depends greatly on the situation we are looking at.