What is the best point estimate for the population mean?
Understand the Problem
The question is asking for the best point estimate for the population mean, which typically refers to using sample data to estimate the average of a larger population. The common approach is to use the sample mean as the point estimate.
Answer
The point estimate for the population mean is $\bar{x} = 6$.
Answer for screen readers
The point estimate for the population mean is $\bar{x} = 6$.
Steps to Solve
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Identify the Sample Data To find the point estimate for the population mean, we need to collect the sample data. For example, let's say we have a sample of five data points: $x_1 = 2, x_2 = 4, x_3 = 6, x_4 = 8, x_5 = 10$.
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Calculate the Sample Mean The sample mean ($\bar{x}$) is calculated by adding all the sample values together and dividing by the number of samples (n).
First, sum the values: $$ \text{Sum} = x_1 + x_2 + x_3 + x_4 + x_5 = 2 + 4 + 6 + 8 + 10 = 30 $$
Now, divide by the number of samples: $$ \bar{x} = \frac{\text{Sum}}{n} = \frac{30}{5} = 6 $$
- State the Point Estimate The point estimate for the population mean will be this calculated sample mean. In our example, it is $6$.
The point estimate for the population mean is $\bar{x} = 6$.
More Information
The sample mean is the best point estimate for the population mean because it provides a simple and unbiased estimate when the sample is representative of the population.
Tips
- Forgetting to divide by the correct number of samples (n), which would lead to an incorrect mean.
- Using a non-representative sample can distort the point estimate.
