Central Tendency in Statistics

Central tendency is a statistical measure that identifies a single value as representative of an entire dataset. It describes the central position of a frequency distribution. The goal is to find a number that best summarizes all observations, giving insight into where most values tend to cluster.

The three primary measures of central tendency are Mean, Median, and Mode.

1. Mean (Arithmetic Mean):
   It is the sum of all observations divided by the total number of observations.

1. • Example (Real life): In a company, if five employees earn ₹25,000, ₹30,000, ₹35,000, ₹40,000, and ₹70,000,
   • Mean Salary = (25000+30000+35000+40000+70000)/5 = 40000

This gives the average salary of the group.

1. • Limitation: It is sensitive to outliers (e.g., one extremely high salary can raise the mean).
2. Median:
   The median is the middle value when data is arranged in ascending or descending order.
   • If the number of observations is odd, the median is the middle value.
   • If even, it’s the average of the two middle values.
   • Example: The median household income in a city helps show the income level of a typical family, unaffected by very rich or very poor households.
3. Mode:
   The mode is the value that appears most frequently in a dataset.
   • Example: In a shoe store, if most customers buy size 8, then size 8 is the mode — it represents the most common shoe size.

In summary:

• Mean = mathematical average (used in performance analysis, finance, etc.)
• Median = middle value (used in income data, property prices)
• Mode = most frequent value (used in marketing, product design, etc.)