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What is the mode of the following data?
61, 71, 71, 87, 74, 67, 79, 83, 68, 88, 81, 80, 71, 73, 72, 87, 60, 86, 83, 68, 79, 84, 88, 65, 63
79
68
71
87
71
Shortcut Trick Mode is the value that appears most frequently in the given data set. Count occurrences of each value: 71 appears 3 times. Other values like 68, 79, 83, 87, and 88 appear only 2 times. The value with the maximum frequency is 71. ∴ T...
Shortcut Trick
Mode is the value that appears most frequently in the given data set.
Count occurrences of each value: 71 appears 3 times.
Other values like 68, 79, 83, 87, and 88 appear only 2 times.
The value with the maximum frequency is 71.
∴ The correct answer is 71.
Alternate Method
Given Data: 61, 71, 71, 87, 74, 67, 79, 83, 68, 88, 81, 80, 71, 73, 72, 87, 60, 86, 83, 68, 79, 84, 88, 65, 63
Formula: Mode = Observation with the highest frequency
⇒ Frequency count of distinct values:
⇒ 60, 61, 63, 65, 67, 72, 73, 74, 80, 81, 84, 86 ⇒ each occurs 1 time
⇒ 68, 79, 83, 87, 88 ⇒ each occurs 2 times
⇒ 71 ⇒ occurs 3 times
⇒ Maximum frequency = 3
⇒ Mode = 71
∴ The correct answer is 71.
Additional Information
Arithmetic Mean
The average of the data set, calculated as Sum of all observations ÷ Total number of observations.
Median
The middle value when data is arranged in ascending or descending order. For n observations, if n is odd, Median = ((n+1)/2)th term.
Empirical Relationship
The relation between three measures of central tendency: Mode = 3 × Median − 2 × Mean.
Bimodal and Multimodal
A data set with two modes is called bimodal, and a set with more than two modes is called multimodal.