The coefficient of skewness measures how much the distribution of a sample differs from symmetry. A perfectly symmetric distribution will have a skewness of 0. If the skewness coefficient is significantly greater than 0, then the distribution is right-skewed. If the skewness coefficient is significantly less than 0, then the distribution is left-skewed The skewness coefficient for a sample of values x1, T2, . . . ,Tm is defined as 7l skew- 3/2 where =- 72 Xi Is the sample mean (a) Write a function with one argument to compute the skewness for any numeric input vector. (b) Use your function to compute the skewness of Andy's commute times from Question 6. Interpret your answer Note: Use Andy's data after fixing the mistake mentioned in 6(c) (c) Through algebraic manipulation, a one-pass formula for the coefficient of skewness is Tt n. v | .r-ZF.zf+2nr3 skew = Write a function with one argument to compute the skewness for any numeric input vector using the one-pass formula. Verify that your new function gives the same answer as your function from (a) (d) Multiply the commute times by 1010 (1e10) and compute the skewness on the new vector using both of your skewness functions. Do your results differ from your answers in (b) and (c)? Explain intuitively or nathematically why or why not. The coefficient of skewness measures how much the distribution of a sample differs from symmetry. A perfectly symmetric distribution will have a skewness of 0. If the skewness coefficient is significantly greater than 0, then the distribution is right-skewed. If the skewness coefficient is significantly less than 0, then the distribution is left-skewed The skewness coefficient for a sample of values x1, T2, . . . ,Tm is defined as 7l skew- 3/2 where =- 72 Xi Is the sample mean (a) Write a function with one argument to compute the skewness for any numeric input vector. (b) Use your function to compute the skewness of Andy's commute times from Question 6. Interpret your answer Note: Use Andy's data after fixing the mistake mentioned in 6(c) (c) Through algebraic manipulation, a one-pass formula for the coefficient of skewness is Tt n. v | .r-ZF.zf+2nr3 skew = Write a function with one argument to compute the skewness for any numeric input vector using the one-pass formula. Verify that your new function gives the same answer as your function from (a) (d) Multiply the commute times by 1010 (1e10) and compute the skewness on the new vector using both of your skewness functions. Do your results differ from your answers in (b) and (c)? Explain intuitively or nathematically why or why not
