Question

Which of the following is/are true about parameter ?
A. It is a characteristic of a sample.
B. It is a characterstic of a population.
C. It is a numerical value that is taken from the entire population, such as the population mean.
D. It is the numerical value taken from a sample and calculated from the sample observations alone.
Choose the correct answer from the options given below:

• A. A only
• B. B and D only
• C. B and C only
• D. A and D only

Hint:

A parameter describes the whole population. A number computed from a sample is called a statistic.

Answer 1

The Correct Option is C

Step 1: Idea:
Sort each statement by asking one question: does the number come from the whole population or from a sample? Population numbers are parameters. Sample numbers are statistics.

Step 2: Use symbols.
The population mean is written $\mu$ and the population standard deviation is $\sigma$. These are parameters. The sample mean $\bar{x}$ and sample standard deviation $s$ are statistics.

Step 3: Test A and D.
Both A and D talk about a sample. Anything that belongs to a sample, or is computed only from sample data, is a statistic. So A and D are wrong.

Step 4: Test B and C.
B says a parameter is a characteristic of a population. C says it is a value taken from the entire population, like the population mean. Both agree with the definition, so both are right.

Step 5: Read the options.
The pair that has exactly B and C is option 3. Options 1, 2 and 4 each contain a statement about a sample, so they fail.

Final Answer:
The correct statements are B and C. \[ \boxed{\text{B and C only}} \]