• Sampling vs. Non-Sampling Errors:
• Sampling Error: Arises solely from observing a sample rather than the complete population; absent in a complete census.
• Non-Sampling Error: Arises from human errors, ambiguity in definitions, faulty instruments, non-response, measurement and recording mistakes, and tabulation errors.
• Because these operational factors can occur whenever data is collected, non-sampling errors are present in both sample surveys and complete censuses.
• Conclusion: Non-sampling errors are present both in sample surveys and census (Option 2).

Correct option: (2) Non-sampling errors are present both in sample surveys and census

• Parameters of Binomial Distribution:
• For a binomial distribution with $n$ trials and success probability $p$:

where $q = 1 - p$.

• Dividing variance by mean:

• The probability of success $p$ is:

• (Additionally, total trials $n = \frac{\text{Mean}}{p} = \frac{7}{1/7} = 49$).
• Conclusion: The probability of success $p$ is 1/7 (Option 3).

Correct option: (3) 47

• Choice of Central Tendency for Product Sizing:
• To market a manufactured consumer good (such as talcum powder, footwear, or ready-made garments) in a single size, the manufacturer aims to satisfy the maximum number of consumers.
• The Mode represents the value that occurs with greatest frequency in the distribution (the most popular and widely purchased size).
• Therefore, marketing decisions on product sizes are based on the Mode.
• Conclusion: Mode (Option 3).

Correct option: (3) Mode

• Correlation Between Complementary Counts in Coin Tosses:
• In $n$ tosses of a coin, every toss results in either a head or a tail:

• The random variable $Y$ is an exact deterministic linear function of $X$ with a strictly negative slope:

• Correlation Coefficient Calculation:

• Because $X$ and $Y$ have a perfect inverse linear relationship, the correlation coefficient is identically -1.
• Conclusion: The correlation is -1 (Option 4).

Correct option: (4) A