Two data sets of 23 integers each are summarized in the histograms shown. For each of the histograms,the first interval represents the frequency of integers greater than or equal to 10, but less than 20. Thesecond interval represents the frequency of integers greater than or equal to 20, but less than 30, and soon. What is the smallest possible difference between the mean of data set A and the mean of data set B?
Correct answer: B. 1
- A. 0
- B. 1
- C. 10
- D. 23
Explanation
The histograms presented show that Data Set A has higher overall values compared to Data Set B. By assigning the lowest values to A's intervals and the highest to B's, the smallest possible difference in means is calculated to be 1. This is achieved when the frequencies are almost equal but differ slightly in adjacent intervals, resulting in a very small mean difference. Therefore, option B is the correct answer. The other options are incorrect as they either consider theoretical equality, extreme shifts in value ranges, or the maximum possible difference in sums rather than focusing on the smallest possible mean difference between the two data sets.
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