位置24的问题 In constructing a frequency distribution, as the number of classes is decreased, the class width can increase or decrease depending on the data values.TrueFalse

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BlackTom AI · Accepted Answer

Question restatement: In constructing a frequency distribution, as the number of classes is decreased, the class width can either increase or decrease depending on the data values. True or False?

Option 1: True. This claim is not accurate. When you reduce the number of classes while keeping the data range (minimum to maximum) effectively the same, the class width tends to increase, not vary arbitrarily with the data values. The width is determined by range divided by the number of classes, so fewer classes usually mean wider intervals; data values themselves do not cause the width to flip between increasing and decreasing in a inconsistent way.

Option 2: False. This statement is correct. If you hold the overall data range constant, decreasing the number of classes forces the class width to become larger on average. The class width is essentially (max − min) divided by the number of classes; fewer classes produce a larger quotient, hence wider classes. Although you could adjust class endpoints manually, the typical behavior under a fixed range is an increase in width when the class count drops, not a data-value–dependent fluctuation.

Summary of common misconceptions: Some learners think the width could go up or down depending on where the data cluster, but the formal relationship is governed by the range and the number of classes rather than the specific distribution of values within the range. If you increase the number of classes, the width decreases; if you decrease the number of classes, the width increases (assuming the range is fixed).

位置24的问题 In constructing a frequency distribution, as the number of classes is decreased, the class width can increase or decrease depending on the data values.TrueFalse

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