Video: Selecting a Statistical Measure That Matches Given Changes When Removing a Data Value from a Data Set

Last month, Daniel scored 82, 61, 86, and 82 in his English quizzes. If his lowest score was to be dropped, which of the following would increase? [A] Mean [B] Median [C] Mode

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Video Transcript

Last month, Daniel scored 82, 61, 86, and 82 in his English quizzes. If his lowest score was to be dropped, which of the following would increase. Is it A) mean, B) median, or C) mode?

In order to answer this question, we can calculate the mean, median, and mode before the score was dropped and after the score was dropped. In order to calculate the mean from a data set, we firstly add all the values, in this case, 82, 61, 86, and 82. We then divide this total by the number of values we have, in this case, four. The total, or sum, of Daniel’s scores is 311. Dividing this by four gives us a mean of 77.75.

Daniel’s lowest score is being dropped. This is 61. In order to calculate the mean after this has been dropped, we add 82, 86, and 82 and then divide by three. This is equal to 84.6 recurring. When Daniel’s lowest score is dropped, his mean has increased from 77.75 to 84.6 recurring. This suggests that mean is the correct answer. It is, however, worth checking whether the median and mode have increased or decreased.

In order to work out the median, we order the values from smallest to largest or largest to smallest. We then find the middle number. As there are an even number of values, there will be two middle numbers. As these are both equal to 82, the median before the lowest score was dropped is 82. After the lowest score is dropped, Daniel has values of 82, 82, and 86. Once again, the median is equal to 82. Daniel’s median score has, therefore, not increased.

The mode is the most frequently occurring value. In both cases, before and after the lowest score was dropped, the mode was 82. This is because the score 82 occurred more often than any other score. We can, therefore, conclude that when Daniel’s lowest score was dropped, the median and mode remain the same, but the mean increased.

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