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 = 2.1 ), median = 19 is ( p = square ). (round to the nearest hundredth as needed.)

Explanation:

Step1: Identify the formula and values

We are given the formula for skewness \( P=\frac{3(\bar{x}-\text{median})}{s} \), with \( \bar{x} = 18 \), \( \text{median}=19 \), and \( s = 2.1 \).

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 \( s \): \( \frac{-3}{2.1}\approx - 1.43 \) (rounded to the nearest hundredth).

Answer:

\( -1.43 \)