Mean, Median, Mode

Enter Your Data

📚 How It Works

Mean (Average)

The arithmetic mean is the sum of all values divided by the count:

Mean = (Σx) / n

Example: For data [10, 15, 20, 25], Mean = (10+15+20+25) / 4 = 70 / 4 = 17.5

• Pros: Uses all data points, easy to calculate
• Cons: Sensitive to outliers (extreme values)
• Best for: Symmetric distributions, no extreme outliers

Median (Middle Value)

The median is the middle value when data is sorted:

• Odd count: Middle value (position = (n+1)/2)
• Even count: Average of two middle values

Example: For [10, 15, 20, 25, 30], Median = 20 (middle value)

Example: For [10, 15, 20, 25], Median = (15+20) / 2 = 17.5

• Pros: Not affected by outliers, represents center
• Cons: Doesn't use all data points
• Best for: Skewed distributions, data with outliers (like income)

Mode (Most Common)

The mode is the value(s) that appear most frequently:

• Unimodal: One mode (one peak)
• Bimodal: Two modes (two peaks)
• Multimodal: More than two modes
• No mode: All values appear equally (or all unique)

Example: For [1, 2, 2, 3, 4, 4, 4, 5], Mode = 4 (appears 3 times)

• Pros: Shows most typical value, works with categorical data
• Cons: May not exist or be useful
• Best for: Categorical data, finding most popular item

When to Use Each Measure

Situation	Best Measure	Reason
Test scores (no outliers)	Mean	Uses all data, fair representation
House prices	Median	Not skewed by mansions/outliers
Shoe sizes	Mode	Most common size to stock
Income data	Median	Billionaires skew mean
Survey ratings (1-5)	Mode or Median	Ordinal categorical data

Other Descriptive Statistics

• Range: Max - Min (spread of data)
• Midrange: (Max + Min) / 2 (center of range)
• Sum: Total of all values
• Count: Number of data points

Real-World Applications

• Education: Average test scores, grade distributions
• Business: Average sales, most popular products
• Healthcare: Average patient age, common symptoms
• Economics: Median income, average prices
• Sports: Average scores, batting averages