There are three sets of data, each having six observations. The median of all three sets is the same, and it is
also the same as the mode for all three sets. Based on this information, which of the following statement(s)
is/are true?
O O O O
С C
Statement I: All three sets have the same mean, which is always the same as the median and the mode.
Statement II: If we combine all eighteen observations into one dataset, then the mode and the median of
the combined dataset will be the same as the mode and the median of the three initial datasets.
Answers
Answer:
In combinatorics, a branch of mathematics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as
Venn diagram showing the union of sets A and B as everything not in white
{\displaystyle |A\cup B|=|A|+|B|-|A\cap B|,}|A\cup B|=|A|+|B|-|A\cap B|,
where A and B are two finite sets and |S| indicates the cardinality of a set S (which may be considered as the number of elements of the set, if the set is finite). The formula expresses the fact that the sum of the sizes of the two sets may be too large since some elements may be counted twice. The double-counted elements are those in the intersection of the two sets and the count is corrected by subtracting the size of the intersection.