The English statistician Karl Pearson (1857-1936) introduced a formula for the skewness of a distribution. P =

The English statistician Karl Pearson (1857-1936) introduced a formula for the skewness of a distribution.

Most distributions have an index of skewness between -3 and 3 . When $P>0$, the data are skewed right. When $P<0$, the data are skewed left. When $P=0$, the data are symmetric. Calculate the coefficient of skewness for each distribution. Describe the shape of each.

(a) $\overline{x}=17,s=2.3$, median $=19$

(b) $\overline{x}=32,s=5.1$, median $=25$

(c) $\overline{x}=9.2,s=1.8$, median $=9.2$

(d) $\overline{x}=42,s=6.0$, median $=40$

(e) $\overline{x}=155,s=20.0$, median $=175$