Question

for a group of 20 items, sigma x = 1452, x^2 = 144280 and mode =63.7. find the coefficient of skewness

Answer 1

i am not really sure

Answer 2

Given are the values of the sum of x, the sum of x^2, and the mode of the data items, Find the coefficient of skewness.

Explanation:

• The coefficient of skewness is the measure of the symmetry of a curve for a given distribution.
• For negative, positive, and zero values of the coefficient the distribution is left-skewed, right-skewed, and symmetrical respectively.
• For a data set having mean $\mu$, standard deviation $\sigma$, and mode $M_o$ the coefficient of skewness is given by, $Sk=\frac{\mu - M_o}{\sigma}$  
• Now we have $N=20,\ \sum x=1452,\ \sum x^2=144280,\ M_o=63.7$
• Hence the mean of the data is, $\mu=\frac{\sum x}{N}=\frac{1452}{20} \ \ \ \ \ \ \ ->\mu=72.6$
• Now the variance of the data is,  
•                                  $\sigma^2=\frac{\sum x^2}{N}-\mu^2 = \frac{144280}{20}-(72.6)^2 \ \ \ \\\ ->\sigma^2=1943.24$  
• Hence, the standard deviation of the data is,  $\sigma=\sqrt{1943.24}\ \ \ \ ->\sigma=44.08$    
• Now the coefficient of skewness is ,
•                                 $Sk_1=\frac{\mu-M_o}{\sigma} \\->Sk_1=\frac{72.6-63.7}{44.08} \\->Sk_1=0.202(approx.)$  
• The coefficient of skewness for the given data items is approximately $0.202$.