Question

(3 pts) Given sample statistics for two data sets: _ Set A: x 23 Med 22 S 1.2 _ Set B: x 24 Med 29 S 3.1 a) Calculate the Pearson’s Index of Skewness for both sets. 3 b) Based on your findings, what type of distribution each set has (circle correct answer): Set A: symmetric skewed left skewed right uniform Set B: symmetric skewed left skewed right uniform c) Which set, A or B, can be considered and analyzed as symmetric _______

Answer 1

Answer:

Step-by-step explanation:

Given Data:

Set A :        x = 23,       Med = 22,             S = 1.2

Set B :        x = 24,       Med = 29,             S = 3.1

The Formula for Pearson's Index of Skewness (for Median in given data) is:

$Sk_{2} = 3(\frac{x - Med}{S} )$

where,

$Sk_{2} =$ Pearson's Coefficient of Skewness

$Med =$ Median of Distribution

$x=$ Mean of Distribution

$S=$ Standard Deviation of Distribution

a) Finding Skewness:

For Set A:

$Sk_{2_{A}} = 3(\frac{23 - 22}{1.2} )\\\\Sk_{2_{A}} = (\frac{3}{1.2} )\\\\Sk_{2_{A}} = 2.5$

For Set B:

$Sk_{2_{B}} = 3(\frac{24 - 29}{3.1} )\\\\Sk_{2_{B}} = 3(\frac{-5}{3.1} )\\\\Sk_{2_{B}} = -4.84$

b) Type of Distribution:

For Set A:

As the value of skewness is a positive value (i.e. 2.5). Hence, Set A is right (positively) skewed.

For Set B:

As the value of skewness is a negative value (i.e. -4.84). Hence, Set B is skewed left (or negatively skewed).

c) Which Set can be considered as symmetric?

As the Pearson's Coefficient of skewness for Set A (2.5) is closer to 0 as compared to that of Set B (-4.84). Set A is more closer to that of a symmetric distribution and therefore can be considered as one.