The condition of scores being distorted in one direction or the other (towards the ends of the distribution) within a given distribution of data is known as
a skew.
The condition you're describing is called skewness. Skewness measures the asymmetry of a distribution in terms of the tail behavior. It determines if the data is skewed to the left (negative skew) or to the right (positive skew).
To determine skewness, you can follow these steps:
1. Calculate the mean (μ) and standard deviation (σ) of the data.
2. Find the difference between each data point and the mean.
3. Cube each difference (raise to the power of 3).
4. Sum all the cubed differences.
5. Divide the sum by the product of the standard deviation cubed (σ³).
6. Calculate the cube root of the result obtained in step 5.
The resulting value will be the skewness coefficient. If the coefficient is positive, it indicates positive skew (tail on the right), while a negative coefficient indicates negative skew (tail on the left). A value close to zero denotes a symmetric distribution.
Note that skewness can also be estimated using statistical software or programming languages that have built-in functions for calculating skewness.