Question

The following data are from a simple random sample: 3 , 7 , 4 , 12 , 4 , 12. The point estimate of the population mean is,

• A. 42
• B. 7
• C. 24
• D. 6

Hint:

The sample mean is the point estimate of the population mean. Add all values and divide by 6.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A point estimate is a single number used to guess a population value. The best point estimate of the population mean is the sample mean \(\bar{x}\).

Step 2: Key Formula or Approach:
\[ \bar{x} = \frac{\sum x}{n} \]

Step 3: Add the values.
\[ 3+7+4+12+4+12 = 42 \]

Step 4: Divide by the sample size.
There are 6 values. So \[ \bar{x} = \frac{42}{6} = 7 \]

Step 5: Check the options.
42 is only the sum of the values, not the mean. 24 and 6 do not match the calculation. 7 is correct, which is option 2.

Final Answer:
The point estimate of the population mean is 7, which is option 2. \[ \boxed{7} \]