Let's analyze each statement to determine its correctness:

(i) Inferential statistics can be used for rigorous comparisons between two populations.

• True. Inferential statistics involves using sample data to make conclusions or inferences about populations, including rigorous comparisons (e.g., t-tests, ANOVA, etc.).

(ii) Mean is the best measure of central tendency for data of all distribution.

• False. The mean is sensitive to outliers and skewed data, so it is not always the best measure. For skewed distributions, the median is often a better measure of central tendency.

(iii) Mean cannot be calculated for nominal types.

• True. Nominal data represents categories without a numerical relationship, so mean calculation is not possible (e.g., colors, names).

(iv) Each data set has one and only one mode.

• False. A data set can have no mode (if no number repeats) or multiple modes (if multiple numbers repeat with the same highest frequency).

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Correct Answer:

B. (i) and (iii)

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Would you like further details or explanations for any specific statement? Here are five related questions for exploration:

1. How does inferential statistics differ from descriptive statistics?
2. What are the advantages of using the median over the mean in skewed data?
3. Can the mode be useful in continuous data distributions? Why or why not?
4. How do nominal, ordinal, and interval data differ in terms of statistical analysis?
5. What are some statistical measures suitable for analyzing categorical data?

Tip: Always check the nature of your data (nominal, ordinal, interval, or ratio) before deciding which statistical measure to apply!