Question

the 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} = 18 \\), \\( s = 2.8 \\), median \\( = 19 \\) is \\( p = \square \\).
(round to the nearest hundredth as needed.)

Explanation:

Step1: Identify the formula and values

We use the formula \( P=\frac{3(\bar{x}-\text{median})}{s} \), where \( \bar{x} = 18 \), median \( = 19 \), and \( s = 2.8 \).

Step2: Substitute the values into the formula

First, calculate \( \bar{x}-\text{median} \): \( 18 - 19=-1 \).
Then, multiply by 3: \( 3\times(-1) = -3 \).
Finally, divide by \( s \): \( \frac{-3}{2.8}\approx - 1.07 \).

Answer:

\( -1.07 \)