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The mode of the following data: 5, 8, 5, 7, 8, 5, 9, 5, 2, 8 is:
5
8
7
9
5
Use a tally table or cross off numbers quickly; count the frequency of each distinct number by scanning the sequence once, focusing on the ones appearing most often.
A data set of ten observations: 5, 8, 5, 7, 8, 5, 9, 5, 2, 8.
Mode=Value┬аwith┬аthe┬аmaximum┬аfrequency
Use a tally table or cross off numbers quickly; count the frequency of each distinct number by scanning the sequence once, focusing on the ones appearing most often.
Many students mistake the 'median' (middle value) for the 'mode' (most frequent value) or miscount the occurrences of numbers that look similar like 5 and 8.
Tabulate frequencies
List each unique value and count how many times it appears in the given data set.
5:4┬аtimes,8:3┬аtimes,7:1┬аtime,9:1┬аtime,2:1┬аtime
Identify the maximum
Compare the frequencies calculated to find the value with the highest count.
Max┬аfrequency=4
Select the mode
Identify the number associated with the maximum frequency.
Mode=5
A is correct because the number 5 appears four times, which is more frequent than any other number in the set.
In larger data sets, this is known as the 'Modal Class' concept in grouped frequency distributions, often linked with the Mean and Median through the empirical formula 3├ЧMedian=Mode+2├ЧMean.
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