Histogram Analysis under Transformations

00:00 8 marks

Consider a histogram representing a frequency distribution of exam scores. The histogram consists of equal-width bins and clearly indicates the modal class, skewness, and presence of potential outliers.

Part a

5 minutes 4 marks

Question

Describe the key features of the original histogram. Discuss the modal class, the distribution’s skewness, and note any potential outliers or unusual patterns that might be present. Base your answer on the typical characteristics of a histogram built from exam score data.

Hint Hint

Hint

Identify the frequency peak, symmetry or skewness, and any data gaps or extra-high values.

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Complete Answer

The original histogram typically shows a clear modal class represented by the highest bar, may exhibit a skewed distribution (either left or right), and any bars isolated from the main cluster can be noted as potential outliers.

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Part b

5 minutes 4 marks

Question

Suppose the bin widths of the given histogram are uniformly increased by a factor of 2. Explain how this scaling affects the histogram’s appearance, particularly addressing any changes to bin heights, the spread of the distribution, and the visual interpretation of data density.

Hint Hint

Hint

Consider how frequency density changes when the bin width is altered. Remember that the area of the bars represents frequency.

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Complete Answer

Doubling the bin widths will halve the bin heights if we are maintaining the frequency density representation. The overall shape and skewness will appear similar, but the horizontal axis scale is stretched, making the distribution appear wider.

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