Given the sample dataGiven the sample $x_1 = 14$, $x_2 = 3$, $x_3 = 6$, and $x_4 = 19$, let's compute each part step by step.

a. Find $n$

$n$ is the number of data points in the sample. In this case, there are four values: $x_1, x_2, x_3, x_4$.

So, $n = 4$.

b. Compute $\sum x_i$

The summation $\sum x_i$ means the sum of all the data points:

$\sum x_i = x_1 + x_2 + x_3 + x_4$ $\sum x_i = 14 + 3 + 6 + 19 = 42$

So, $\sum x_i = 42$.

c. Determine $\overline{x}$ (the mean)

The mean $\overline{x}$ is the sum of all the data points divided by the number of data points $n$:

$\overline{x} = \frac{\sum x_i}{n}$ $\overline{x} = \frac{42}{4} = 10.5$

So, the mean $\overline{x} = 10.5$.

Final Answers:

a. $n = 4$
b. $\sum x_i = 42$
c. $\overline{x} = 10.5$

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Do you need further clarification or more details? Here are five related questions to expand on this:

1. What would happen to the mean if another data point was added?
2. How is the summation symbol used in other statistical calculations?
3. Can the mean alone describe a data set completely?
4. What is the relationship between the mean and the median in this data?
5. How do outliers affect the mean?

Tip: When computing the mean, always verify the number of data points to ensure accuracy.