Question

The value which occurs most frequently in a data set is called:

• A. Mean
• B. Median
• C. Mode
• D. None

Hint:

Remember:
• Mean \(\rightarrow\) Average
• Median \(\rightarrow\) Middle value
• Mode \(\rightarrow\) Most frequent value Both “Mode” and “Most” start with “Mo”.

Answer 1

The Correct Option is C

Concept: In statistics, measures of central tendency are used to represent the central or typical value of a data set. The three major measures of central tendency are:
• Mean — Arithmetic average of all observations
• Median — Middle value of the arranged observations
• Mode — Observation occurring with the highest frequency The mode identifies the most repeated or most common observation in the data.

Step 1: Understanding the meaning of Mean.
Mean is calculated using: \[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \] It gives the average value of the data. However, the mean does not necessarily represent the most repeated observation. Therefore, Mean is not the correct answer.

Step 2: Understanding the meaning of Median.
Median is the middle value after arranging the data in ascending or descending order. For example: \[ 2,\ 4,\ 5,\ 8,\ 10 \] the median is: \[ 5 \] Median represents the positional center of the data, not the most frequently occurring value. Hence, Median is not correct.

Step 3: Understanding the meaning of Mode.
Mode is defined as the observation that appears most frequently in a data set. For example: \[ 2,\ 3,\ 3,\ 5,\ 7,\ 9 \] Here: \[ 3 \] appears twice, while all other numbers appear only once. Therefore: \[ \text{Mode} = 3 \] Thus, the value occurring most frequently is called the Mode.

Step 4: Checking the given options carefully.
Option (1): Mean Incorrect. Option (2): Median Incorrect. Option (3): Mode Correct. Option (4): None Incorrect. Final Conclusion: The value occurring most frequently in a data set is called: \[ \boxed{\text{Mode}} \] Hence, the correct answer is option (3).