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The mode of the observations 20,23,25,30,20,31,32,35,20,41,42,43,20 and 20 is:
30
20
40
35
20
Count the occurrences of each number. The one with the highest count is the mode. 20 appears 5 times, while all other numbers appear only once.
Observations: 20, 23, 25, 30, 20, 31, 32, 35, 20, 41, 42, 43, 20, 20
Mode=value occurring with highest frequency
Count the occurrences of each number. The one with the highest count is the mode. 20 appears 5 times, while all other numbers appear only once.
Students often count incorrectly if the list is not sorted. It is helpful to write out the frequency of each distinct value.
Identify frequency of each observation
List each unique value and count how many times it appears in the sequence.
20:5,23:1,25:1,30:1,31:1,32:1,35:1,41:1,42:1,43:1
Determine the mode
The mode is the observation with the maximum frequency. Comparing the frequencies, 20 occurs 5 times, which is the highest frequency.
Frequencymax=5, for value 20
Final Conclusion
Since 20 is the most frequent value, it is defined as the mode of the given data set.
Mode=20
B is correct because the number 20 appears 5 times in the given list, which is more frequent than any other observation.
This is a fundamental concept in statistics. In more advanced exams, you may be asked for the Empirical Relationship between Mean, Median, and Mode: Mode=3(Median)−2(Mean). Remember this formula as it often appears in shift-based competitive papers.
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