The question asks which of the given statements are features of a bar graph/chart. The statements are: I. This representation displays data in bars of equal size and spacing. II. Frequencies/relative frequencies represent height of bars. III. Bars are arranged in decreasing order of frequency or relative frequency.

1. Problem Description

The question asks which of the given statements are features of a bar graph/chart. The statements are:

I. This representation displays data in bars of equal size and spacing.

II. Frequencies/relative frequencies represent height of bars.

III. Bars are arranged in decreasing order of frequency or relative frequency.

2. Solution Steps

Let's analyze each statement:

Statement I: Bar graphs typically have bars with equal widths (size) and spacing between them for clarity and ease of comparison. So, statement I is true.

Statement II: The height of the bars in a bar graph represents the frequencies or relative frequencies of the categories being represented. So, statement II is true.

Statement III: While bar graphs can be arranged in decreasing order of frequency or relative frequency (often called a Pareto chart), it is not a mandatory feature of all bar graphs. They can be arranged in other orders as well (alphabetical, etc.). So, statement III is not always true, but can be a feature.

Since Statement II appears twice, and we have conflicting interpretations, let us consider which statements *must* be true for a graph to be considered a bar graph.

The height of the bar *must* represent the frequency/relative frequency of that category.

The bars also *must* have the same width. The ordering of the bars is a *optional* element.

However, since statement III has been labeled with "II", we can assume that this is an error, and instead, the correct statement number is III. Thus, we can consider both statements I and II to be correct.

If statement "III" is actually statement "III," it is incorrect.

If statement "III" is actually statement "II", then only statements I and II are correct, which is not an option.

Given the provided multiple choices, the question intends that statement II is correct and statement III (meant to be III) is the only option that applies to sorted bar graphs. Thus, only statement II would be applicable here, because statement I is false if the bar graph has variable bar width, and statement III is false if the bar graph is not sorted.

3. Final Answer

D. None of the above.