Worksheet for Skewness Calculation

Skewness used to find out the asymmetry of the probability distribution of a real-valued random variable. This Math worksheet help you to understand how to calculate the skewness for the given value. The steps to be followed are,

1. Calculate standard deviation and mean
2. Subtract the mean from each raw score
3. Raise each of these deviations from the mean to the third power and sum
4. Calculate skewness, which is the sum of the deviations from the mean, raise to the third power, divided by number of cases minus 1, times the standard deviation raised to the third power


The formula used to calculate skewness is,

For example
To find the skewness whose inputs are 5,20,40,80,100
Total Inputs (N) = 5

Mean:
Mean (x_m) = (x₁+x₁+x₂...x_n )/N
Mean (x_m)= 245/5
Mean (x_m)= 49

Standard deviation:
SD = sqrt(1/(N-1)*((x₁-x_m)²+(x₂-x_m)²+..+(x_n-x_m)²))
   =sqrt(1/(5-1)((5-49)²+(20-49)²+(40-49)²+(80-49)²+(100-49)²))
   =sqrt(1/4((-44)²+(-29)²+(-9)²+(31)²+(51)²))
   =sqrt(1/4((1936)+(841)+(81)+(961)+(2601))
   =sqrt(1605)
   =40.0625


Skewness = ((5 - 49) + (20 - 49) + (40 - 49) + (80 - 49) + (100 - 49))³/ (5 - 1) x (40.0625)³
   = 52140/257201.875
   = 0.2027

Skewness value for the given data is 0.2027

When you try such calculations on your own, this skewness calculator can be used to verify the results of your calculations.