Question

Exercise 5. Three samples of the variable x are collected in three different circumstances: a, b, c. aa 1.65,-5.74, -0.84, -4.50, 12.90, 0.84,-4.73,7.89, 10.72, 4.40) Zb = (-5.34.-6.26, 3.80,-215,-172-7.35, 6.84, 5.92, 1.72, 7.76) Te = (7.05,-0.13.-10.21,-5.44,-6.75,-12.33, 13.76, 21.51, 0.43, 6.14) Using appropriate graphic tools and indices, compare the three groups through their central tendency, variability and symmetry

Answer 1

Boxplot of Xa, Xb, Xc Xb 10 -10 Xc 20 10 -10

From above three box plots we observe that median (central tendency) of three variables are almost  same i.e. 0 and Inter quartile range (i.e. the length box) is maximum for Xc then Xa then Xb. Hence Xc is more variable or disperse than Xa and Xb and Xa is more variable or disperse than Xb. Since Q3-Q2 is almost equal to Q2-Q1 for Xb and Xc hence Xb and Xc are symmetric whereas Q3-Q2>Q2-Q1 for Xa hence Xa is positively skewed.

Here Q1=First quartile, Q2=Median, Q3=third quartile, Q2-Q1=First portion of box, Q3-Q2=2nd portion of box.