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What is the mode of the following data? 66, 69, 83, 69, 84, 74, 71, 83, 69, 84, 73, 83, 69, 71, 84, 74, 83, 66, 74, 71, 83, 66, 90, 90
90
83
74
84
83
Group the numbers by tens and tally them quickly on the scratchpad to find the highest count without writing a formal frequency distribution table.
Data set: 66, 69, 83, 69, 84, 74, 71, 83, 69, 84, 73, 83, 69, 71, 84, 74, 83, 66, 74, 71, 83, 66, 90, 90
Mode=value┬аwith┬аhighest┬аfrequency
Group the numbers by tens and tally them quickly on the scratchpad to find the highest count without writing a formal frequency distribution table.
Counting a number incorrectly because it appears repeatedly in different segments of the long sequence; always cross-verify the total count of numbers.
Count frequencies of each number
List each unique number and count its occurrences in the provided dataset: 66 occurs 3 times, 69 occurs 4 times, 83 occurs 5 times, 84 occurs 3 times, 74 occurs 3 times, 71 occurs 3 times, 73 occurs 1 time, 90 occurs 2 times.
66:3,69:4,71:3,73:1,74:3,83:5,84:3,90:2
Identify the maximum frequency
Comparing all counts, the value 83 appears the most often, with a total frequency of 5.
Frequency(83)=5
Determine the Mode
Since 83 has the highest frequency among all the numbers in the data set, it is the mode.
Mode=83
B is correct because the number 83 appears 5 times, which is the highest frequency in the given data set.
This concept of frequency is foundational for calculating grouped data mean, median, and variance in later chapters of statistics.
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