Question

if \\(x_1, x_2, x_3, \dots, x_n\\) are the \\(n\\) observations of a variable from a population, then what symbol is used for the population mean?

a. \\(\mu\\)
b. \\(\tilde{x}\\)
c. \\(\sigma\\)
d. \\(\bar{x}\\)

Explanation:

⚡ Using what you learned: Population vs. Sample

Step 1: Identify the target parameter

The question asks for the symbol used to represent the population mean when we have \( N \) observations from an entire population:

$$ X_1, X_2, X_3, \dots, X_N $$

Step 2: Compare statistical notation

• Population Mean: Represented by the Greek letter mu, \( \mu \).
• Sample Mean: Represented by \( \bar{x} \) (x-bar).
• Population Median: Often represented by \( \tilde{\mu} \) or \( M \).
• Summation: Represented by the Greek capital letter sigma, \( \Sigma \).

Therefore, the correct symbol for the population mean is \( \mu \).

Answer:

A. \( \mu \)