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 ) 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} = 17 ), ( s = 2.2 ), median = 18 is ( p = square ). (round to the nearest hundredth as needed.)

Explanation:

Step1: Identify the formula and values

We use the formula \( P=\frac{3(\bar{x}-\text{median})}{s} \), with \( \bar{x} = 17 \), median \( = 18 \), and \( s = 2.2 \).

Step2: Substitute the values into the formula

First, calculate \( \bar{x}-\text{median} \): \( 17 - 18=-1 \).
Then, multiply by 3: \( 3\times(-1)= - 3 \).
Finally, divide by \( s \): \( P=\frac{-3}{2.2}\approx - 1.36 \) (rounded to the nearest hundredth).

Answer:

\( -1.36 \)