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In statistics, the Measures of Central Tendency are foundational tools that help summarize a dataset by identifying its center point or typical value. These measures are vital in both academic research and real-world decision-making. For UGC NET candidates, this topic frequently appears in the syllabus under Paper 1 (Teaching & Research Aptitude) and subject-specific papers like Commerce, Economics, and Education.

What Are Measures of Central Tendency?

Measures of central tendency are statistical values that describe the center or average of a dataset. They are used to determine the value around which other data points are distributed.

The three main measures are:

1. Mean
2. Median
3. Mode

Each measure has its own strengths and is useful depending on the nature of the data and the purpose of analysis.

1. Mean (Arithmetic Average)

Formula:

Mean=∑��

Where:

• ∑� = Sum of all observations
• � = Number of observations

Example:
If the marks of five students are 70, 75, 80, 85, and 90, then:

Mean=70+75+80+85+905=80

Advantages:

• Uses all data points
• Widely applicable in further statistical analysis

Disadvantages:

• Affected by extreme values (outliers)

2. Median (Middle Value)

The median is the middle value of a dataset when arranged in ascending or descending order.

Formula:

• If � is odd:

Median=Value of (�+12)�ℎ item

• If � is even:

Median=�/2�ℎ item + (�/2+1)�ℎ item2

Example:
For the dataset: 55, 60, 65, 70, 95
The median = 65 (middle value)

Advantages:

• Not affected by outliers
• Useful for skewed distributions

Disadvantages:

• Does not use all data points

3. Mode (Most Frequent Value)

The mode is the value that appears most frequently in a dataset.

Example:
In the dataset: 45, 50, 50, 55, 60
The mode = 50

Advantages:

• Easy to identify in discrete data
• Can be used for categorical data

Disadvantages:

• May be no mode or multiple modes
• Not always a reliable measure of central value

When to Use Which?

UGC NET Tip:

Be prepared for:

• Numerical questions based on grouped/un-grouped data
• Conceptual differences between mean, median, and mode
• Use of combined mean or weighted average formulas

Sample MCQ:
Which of the following is least affected by extreme values?
A. Mean
B. Median
C. Mode
D. Range
Correct Answer: B. Median

Conclusion

Understanding measures of central tendency is essential for interpreting data effectively. Whether you're analyzing test scores, income levels, or survey results, these measures provide a quick insight into the data’s core behavior. For UGC NET, not only should you understand how to calculate them, but also when and why each is used.

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