The scores of students in a test are recorded as follows: 4, 3, 3, 2, 1, 2, 5, 7, 8, 3, and 5. Find the mode of the mark.

Analysis

The question asks for the mode of a given set of data. In statistics, the mode is defined as the value that appears most frequently in a data set.

Concept

To find the mode, follow these simple steps:

1. Arrange the data: It is often easier to count the frequency of each number if you list them in ascending order (though not strictly necessary).
2. Count the frequency: Determine how many times each unique number appears in the list.
3. Identify the highest frequency: The number that appears the most times is your mode.

Solution

Given data: 4, 3, 3, 2, 1, 2, 5, 7, 8, 3, 5

Let's list the frequency of each score:

• 1: appears 1 time
• 2: appears 2 times (2, 2)
• 3: appears 3 times (3, 3, 3)
• 4: appears 1 time
• 5: appears 2 times (5, 5)
• 7: appears 1 time
• 8: appears 1 time

Comparing the frequencies:

• 1 occurs once.
• 2 occurs twice.
• 3 occurs three times.
• 4 occurs once.
• 5 occurs twice.
• 7 occurs once.
• 8 occurs once.

Since the number 3 appears more frequently than any other number, it is the mode.

Conclusion

Exam Tip

When you see a list of numbers in an exam, quickly tally them on your rough sheet. Don't just scan with your eyes, as it is very easy to miss one digit and get the wrong answer. A quick frequency table (Score | Tally) will save you from silly mistakes!