The range of the Karl Pearson’s coefficient of skewness (S_k) is: 

Key Points

• Pearson's skewness is calculated by comparing the mean, median, and standard deviation of a distribution. A positive value indicates that the distribution is skewed to the right (tail on the right side), a negative value indicates a left skew (tail on the left side), and a value of zero implies a symmetric distribution.
• Karl Pearson's coefficient of skewness measures the degree of skewness or asymmetry in a probability distribution. It is calculated as 3 times the ratio of the difference between the mean and the median to the standard deviation. \(Sk = {{3 \times (Mean - Median)} \over {Standard \ Deviation}}\)
• The coefficient of skewness can take values between -3 and +3. A positive skewness value indicates a right-skewed distribution, where the tail is on the right side and the majority of the data is concentrated on the left side. A negative skewness value indicates a left-skewed distribution, where the tail is on the left side and the majority of the data is concentrated on the right side. A skewness value of 0 indicates a symmetric distribution.

Hence, the range of Karl Pearson's coefficient of skewness is indeed -3 to +3.