Mean, Median, Mode, Standard Deviation and Variance: Fundamental statistics concepts that are important for Python, Data Science and Machine Learning

Mean, Median, Mode, Standard Deviation and Variance are the fundamental statistics concepts that are important for Python, Data Science and Machine Learning. Let’s break them down step by step:

📊 Key Statistical Terms

1. Mean (Average)
   • Formula: (Sum of values) ÷ (Number of values)
   • Example: (2 + 3 + 7) / 3 = 4
   • It tells us the “central” value.
2. Median (Middle Value)
   • Arrange data in order → pick the middle value.
   • Example: [1, 3, 5] → Median = 3
   • Example: [1, 3, 5, 7] → Median = (3 + 5) / 2 = 4
3. Mode (Most Frequent Value)
   • The number that occurs most often.
   • Example: [2, 2, 3, 4] → Mode = 2
4. Variance
   • The average squared difference from the mean.
   • High variance → data points are spread out.
   • Low variance → data points are close to mean.
5. Standard Deviation (SD)
   • Square root of variance.
   • A measure of spread/dispersion in the same units as data.
   • Low SD → Data points close to mean (tight cluster).
   • High SD → Data points spread widely.

📌 Intuitive Way to Remember

• Mean → Think “average class grade.”
• Median → Think “middle student in a queue.”
• Mode → Think “most popular ice-cream flavor.”
• Variance → Think “how far students’ grades differ from average.”
• Standard Deviation → Think “typical distance from average.”

📈 Graphical Understanding

Here’s what they look like visually:

• Mean → Center of gravity of distribution.
• Median → Splits data into two halves.
• Mode → Peak of the curve (highest frequency).
• Standard Deviation → Width of the curve (spread).

📈 Graphical Relationships

Symmetrical Distribution (Normal Distribution):

Mean, median, and mode are equal and located at the center of the distribution.

Skewed Distribution:

The mean, median, and mode differ. In a positively skewed distribution (tail to the right), the mean is greater than the median, which is greater than the mode. In a negatively skewed distribution (tail to the left), the mean is less than the median, which is less than the mode

Standard Deviation and Spread:

A larger standard deviation indicates a wider spread of data points around the mean.

NOTE: Measures of Central Tendency in Statistics – Central tendencies in statistics are numerical values that represent the middle or typical value of a dataset. Also known as averages, they provide a summary of the entire data, making it easier to understand the overall pattern or behavior. These values are useful because they capture the essence of large datasets in a single, representative number. The three most commonly used measures of central tendency are mean, median, and mode.