What is the mode of the five values 1, 1, 8, 9 and 10?

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Only the value 1 occurs more than once, so it reaches the highest frequency and is the mode, even though the rest of the data are much larger. Choosing 8 favours a value lying among the bulk of the numbers because 1 looks untypical, yet a mode is never required to sit near the bulk of the data.