To calculate the coefficient of skewness $P$, we use the formula introduced by Karl Pearson:

$P = \frac{3(\bar{x} - \text{median})}{s}$

Given dataTo calculate the coefficient of skewness $P$, we use the formula introduced by Karl Pearson:

$P = \frac{3(\bar{x} - \text{median})}{s}$

Given

• Mean $\bar{x} = 17$
• Standard deviation $s = 2.3$
• Median $\text{median} = 18$

Step-by-step calculation:

1. Subtract the median from the mean: $\bar{x} - \text{median} = 17 - 18 = -1$

2. Multiply the result by 3: $3(\bar{x} - \text{median}) = 3(-1) = -3$

3. Divide the result by the standard deviation $s$: $P = \frac{-3}{2.3} \approx -1.30$

Conclusion:

The coefficient of skewness is approximately $P = -1.30$.

Since $P < 0$, this indicates that the data are skewed left.

Would you like further clarification on this, or any details on the steps?

Here are 5 follow-up questions to expand on this:

1. What does a skewness value of 0 signify in a data distribution?
2. How does skewness affect the interpretation of a dataset's mean and median?
3. Can skewness alone determine the normality of a dataset? Why or why not?
4. What are some real-life examples of left-skewed distributions?
5. How would increasing the standard deviation $s$ affect the skewness value?

Tip: Skewness helps assess the symmetry of a dataset. A strong positive or negative skew indicates more extreme values on one side of the distribution.