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What is the mode of the following data?
86, 84, 71, 82, 82, 63, 84, 71, 70, 86, 88, 65, 71, 81, 87, 60, 60, 74, 78, 62, 75, 66, 68, 85, 72
71
86
82
84
71
Write down the data and maintain a frequency count table. Focus on numbers that repeat. Numbers 60, 71, 82, 84, 86 all repeat, so tally them carefully to find the maximum count.
A list of 25 numerical values: 86, 84, 71, 82, 82, 63, 84, 71, 70, 86, 88, 65, 71, 81, 87, 60, 60, 74, 78, 62, 75, 66, 68, 85, 72.
Mode=The value that appears most frequently in a data set
Write down the data and maintain a frequency count table. Focus on numbers that repeat. Numbers 60, 71, 82, 84, 86 all repeat, so tally them carefully to find the maximum count.
Many students miscount the frequency of numbers by missing one entry in a long list; re-verifying the counts of 71, 82, 84, and 86 is crucial.
Tabulate the data
List all unique values and count their occurrences (frequencies) in the dataset.
60:2,62:1,63:1,65:1,66:1,68:1,70:1,71:3,72:1,74:1,75:1,78:1,81:1,82:2,84:2,85:1,86:2,87:1,88:1
Identify frequencies
Compare the counts to find which value appears the most. The number 71 appears 3 times, while others like 82, 84, and 86 appear only 2 times.
f(71)=3
Determine the Mode
Since 71 has the highest frequency of 3, it is the mode of the dataset.
Mode=71
A is correct because 71 is the value that occurs most frequently (3 times) in the provided list of data.
Mode is often useful in identifying the 'most popular' choice or typical value in grouped data, common in statistics and probability questions.
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