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What is the mode of the following data set: 12, 15, 18, 12, 14, 18, 12, 19, 15, 18, 12, 20?
12
15
18
19
12
Use the 'Tally Mark' method: scan the list and write down the numbers as you see them, keeping a count beside each unique number to identify the highest frequency at a glance.
A data set of 12 numbers: 12, 15, 18, 12, 14, 18, 12, 19, 15, 18, 12, 20.
f(x)=count┬аof┬аvalue┬аx
Use the 'Tally Mark' method: scan the list and write down the numbers as you see them, keeping a count beside each unique number to identify the highest frequency at a glance.
Students often mistake the median for the mode, or incorrectly count the frequency of numbers like 18 which also appears multiple times but less frequently than 12.
Identify unique values
List all unique values present in the set: 12,14,15,18,19,20.
S={12,14,15,18,19,20}
Count the frequency of each value
Count how many times each number appears in the original sequence: 12 appears 4 times, 14 appears 1 time, 15 appears 2 times, 18 appears 3 times, 19 appears 1 time, 20 appears 1 time.
Frequency12тАЛ=4,Frequency18тАЛ=3
Determine the mode
The mode is defined as the observation with the highest frequency. Since the value 12 has the maximum frequency of 4, it is the mode.
Mode=12
A is correct because the number 12 appears 4 times in the data set, which is more frequent than any other value.
This concept is fundamental for Data Interpretation (DI) charts; always check for the 'modal class' in grouped frequency distributions to quickly answer questions about the most representative value.