Question

the english statistician karl pearson (1857-1936) introduced a formula for the skewness of a distr
$p = \frac{3(\bar{x} - \text{median})}{s}$
most distributions have an index of skewness between $-3$ and $3$. when $p > 0$ the data are skewe
the data are skewed left. when $p = 0$ the data are symmetric. calculate the coefficient of skewnes
distribution. describe the shape of each.

(a) the coefficient of skewness for $\bar{x} = 18$, $s = 2.1$, median $= 19$ is $p = -1.43$
(round to the nearest hundredth as needed.)
describe the shape of the distribution.
\\(\times\\) a. the data are symmetric.
\\(\circ\\) b. the data are skewed right.
\\(\star\\) c. the data are skewed left.

(b) the coefficient of skewness for $\bar{x} = 32$, $s = 5.8$, median $= 31$ is $p = \square$
(round to the nearest hundredth as needed.)

Explanation:

Step1: Identify the formula

The formula for skewness is \( P=\frac{3(\bar{x}-\text{median})}{s} \). We are given \( \bar{x} = 32 \), \( \text{median}=31 \), and \( s = 5.8 \).

Step2: Substitute the values into the formula

First, calculate \( \bar{x}-\text{median} \): \( 32 - 31=1 \). Then multiply by 3: \( 3\times1 = 3 \). Now divide by \( s \): \( \frac{3}{5.8}\approx0.52 \) (rounded to the nearest hundredth).

Answer:

\( 0.52 \)