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Yes, if there are no values that occur more than once, the mode cannot be used to determine the measure of center. But if there are values that occur frequently the mode can be used. If there are 2 values that occur with the same greatest frequency, this is called bimodal. Multimodal is when there are 3 + values that occur with same greatest frequency.
As stated, no values repeated means the mode cannot be used. The mean is considered to be the most frequently used measure for central of tendency. I think is because we prefer to work with numbers and calculations rather then arranging data into orders. But, the median does find the exact center of data.
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