How to Learn Statistics for Data Science As A Self Starter[ Day - 09 ]

Basics Statistics

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1. Introduction to Basic Terms

2. Variables

3. Random Variables

4. Population, Sample, Population Mean,

Sample Mean

5. Population Distribution, Sample Distribution

and Sampling Distribution

6. Mean, Median ,Mode

7. Range

8. Measure Of Dispersion

9. Variance

10.Standard Deviation

11.Gaussian/Normal Distribution

11. Statistics: Gaussian/Normal Distribution

Introduction

The Gaussian distribution, also known as the normal distribution, is one of the most important concepts in statistics. It is a continuous probability distribution that is symmetric about the mean, meaning that data near the mean are more frequent in occurrence than data far from the mean. The shape of the normal distribution is a bell curve, and it is characterized by its mean (µ) and standard deviation (σ).

Properties of the Normal Distribution

1. Symmetry: The normal distribution is symmetric about the mean. This means that the left half of the curve is a mirror image of the right half.
2. Mean, Median, and Mode: In a normal distribution, the mean, median, and mode are all equal. They are located at the center of the distribution.
3. Bell-Shaped Curve: The normal distribution curve is bell-shaped and has a peak at the mean.
4. Empirical Rule (68-95-99.7 Rule):
5. Asymptotic: The tails of the normal distribution curve approach, but never touch, the horizontal axis. This implies that the distribution extends indefinitely in both directions.

Examples and Problems

Example 1: Suppose the heights of adult men in a city are normally distributed with a mean height of 70 inches and a standard deviation of 4 inches.

Problem 1: What is the probability that a randomly selected man has a height between 66 and 74 inches?

Conclusion

The normal distribution is a fundamental concept in statistics due to its widespread applicability in natural and social sciences. Understanding its properties and how to calculate probabilities, percentiles, and other statistics using the normal distribution is crucial for analyzing data and making informed decisions. By practicing problems related to the normal distribution, one can gain proficiency in applying these concepts to real-world situations...