When forming the classes for frequency distribution and histogram, suppose there were several empty classes. You should:

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When constructing a frequency distribution and its histogram, empty classes indicate that the chosen class interval width is not capturing the data density effectively. Examining each option:
Option 1: 'double the class width' — Increasing width can reduce fragmentation of data across many bins and may help eliminate empty bins by aggregating adjacent ranges. However, simply doubling is an arbitrary choice and could overly lump data, potentially hiding important variation between values. It may solve empties in some datasets but not systematically address the underlying issue of sparse data in specific ranges.
Option 2: 'keep the current class width' — Maintaining the same width when several classes are empty does not address the emptiness problem. Empty classes persist, which means the histogram and distribution remain uninformative about where data actually lie. This option generally fails to improve the representation.
Option 3: 'increase the class width' — Widening the class intervals tends to merge neighboring empty classes with adjacent nonempty ones, reducing or eliminating empty categories and creating a more interpretable distribution. This approach aligns with standard practice when facing empty or sparse bins, especially in exploratory data analysis where the goal is a clearer overall shape of the distribution.
Option 4: 'decrease the class width' — Narrowing the width typically creates more classes, which can exacerbate the problem of empty bins in regions with low frequency. It is unlikely to resolve emptiness and may produce a histogram that's noisier and harder to interpret.
In summary, reducing granularity (increasing width) directly targets the presence of empty classes by aggregating data into fewer, broader categories, whereas keeping width unchanged or decreasing it tends to preserve or worsen the emptiness issue. The idea of just doubling the width (Option 1) is a specific choice of increasing width but does not provide a principled rationale and may not suit all data shapes; the more general and reliable strategy is to increase the width to minimize or remove empty classes.

2025-HS1-FIN60003-Business Statistical Modelling-H1 Mid-semester Test Monday Class

When forming the classes for frequency distribution and histogram, suppose there were several empty classes. You should:

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