What is the mode of the following data: 22, 25, 28, 25, 22, 29... | Mathematics MCQ | Examoogle

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What is the mode of the following data: 22, 25, 28, 25, 22, 29, 25, 22, 30, 25, 28, 22, 25?

Correct Answer

📐 MA • Math Direct ObservationMathematicsStatistics

Option B

Quick Summary:

Create a frequency table by placing a tally mark against each number as you scan from left to right; the one with the longest tally is your mode.

📐MAMath SolutionDirect Observation

📋 Given

A data set containing thirteen numbers: 22, 25, 28, 25, 22, 29, 25, 22, 30, 25, 28, 22, 25.

🔢 Formula Used

Mode=value with maximum frequency\text{Mode} = \text{value with maximum frequency}Mode=value with maximum frequency

⚡ Exam Hall Shortcut / Speed Trick

Create a frequency table by placing a tally mark against each number as you scan from left to right; the one with the longest tally is your mode.

⚠️ Common Student Trap / Pitfall

Students often miscount the number of times 22 and 25 appear, as both have high frequencies, but 25 appears one extra time.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

List the unique values

Identify all unique numbers present in the dataset: $22, 25, 28, 29, 30$ .

Unique Values={22,25,28,29,30}\text{Unique Values} = \{22, 25, 28, 29, 30\}Unique Values={22,25,28,29,30}

Count the frequency of each value

Count how many times each value appears in the dataset: 22 appears $4$ times, 25 appears $5$ times, 28 appears $2$ times, 29 appears $1$ time, and 30 appears $1$ time.

Freq(22)=4,Freq(25)=5,Freq(28)=2,Freq(29)=1,Freq(30)=1\text{Freq}(22)=4, \text{Freq}(25)=5, \text{Freq}(28)=2, \text{Freq}(29)=1, \text{Freq}(30)=1Freq(22)=4,Freq(25)=5,Freq(28)=2,Freq(29)=1,Freq(30)=1

Determine the mode

The mode is defined as the value with the highest frequency. Comparing the frequencies, 25 has the maximum frequency of 5.

Max frequency=5  ⟹  Mode=25\text{Max frequency} = 5 \implies \text{Mode} = 25Max frequency=5⟹Mode=25

✅

B is correct because the number 25 appears 5 times in the dataset, which is more frequent than any other value.

Core Concepts Used

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Frequency Distribution Measures of Central Tendency Mode Identification

💡 EXAM TIP

This concept of frequency is the foundation for calculating Mean in grouped data distributions using the formula $\overline{x} = \frac{\sum f_i x_i}{\sum f_i}$ .

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