Question

english statistician karl pearson (1857 - 1936) introduced a formula for the skewness of a distribution.
p=\frac{3(\bar{x}-\text { median })}{s}
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) the coefficient of skewness for ( \bar{x}=16, s = 2.7 ), median ( = 17 ) is ( p=-1.11 ).
(round to the nearest hundredth as needed.)
describe the shape of the distribution.
a. the data are skewed left.
b. the data are skewed right.
c. the data are symmetric.
(b) the coefficient of skewness for ( \bar{x}=32, s = 5 ), median ( = 31 ) is ( p=) (round to the nearest hundredth as needed.)

Explanation:

Step1: Substitute the values into the formula

Given the formula \(P=\frac{3(\bar{x}-\text{median})}{s}\), substitute \(\bar{x} = 32\), \(s = 5\), and median \(=31\) into it.
We get \(P=\frac{3(32 - 31)}{5}\).

Step2: Calculate the numerator

First, calculate \(32-31=1\). Then multiply by 3: \(3\times1 = 3\).
So the formula becomes \(P=\frac{3}{5}\).

Step3: Calculate the final value

\(P=\frac{3}{5}=0.6\)

Answer:

\(0.6\)