Given the data set: 12, 7, 4, 9, 0, 7, 3. a) Compute mean, median, and mode. b) Calculate Karl Pearson's coefficient of skewness and describe its shape.

The sum of the data points is $\sum x = 0 + 3 + 4 + 7 + 7 + 9 + 12 = 42$.

$$\text{Mean} (\bar{x}) = \frac{\sum x}{n} = \frac{42}{7} = 6$$

The sorted data is $0, 3, 4, 7, 7, 9, 12$.
Since $n=7$ is an odd number, the median is the $\frac{n+1}{2}$-th value, which is the $\frac{7+1}{2} = 4$-th value.
The 4th value in the sorted data is 7.

$$\text{Median} = 7$$

The mode is the value that appears most frequently in the data set. In the given data, the value 7 appears twice, which is more than any other value.

$$\text{Mode} = 7$$

a) Mean = $\boxed{\text{6}}$, Median = $\boxed{\text{7}}$, Mode = $\boxed{\text{7}}$

b) Calculate Karl Pearson's coefficient of skewness of the data set and also describe its shape.

First, calculate the sum of squared differences from the mean: $\sum (x - \bar{x})^2$.
We found $\bar{x} = 6$.

$$(0-6)^2 = 36$$ $$(3-6)^2 = 9$$ $$(4-6)^2 = 4$$ $$(7-6)^2 = 1$$ $$(7-6)^2 = 1$$ $$(9-6)^2 = 9$$ $$(12-6)^2 = 36$$

The sum is $\sum (x - \bar{x})^2 = 36 + 9 + 4 + 1 + 1 + 9 +