#Stats

1.1 Statistics

• Statistics is the science of collecting, organizing and analyzing the data.
• Used for decision making process
• Data - facts or pieces of information

1.2 Types of Statistics

• Descriptive stats
  • It consists of organizing and summarizing the data.
• Inferential stats
  • It consists of using data you have measured to form conclusion, make predictions.
  • By using sample-data make conclusion on population-data

2.1 Covariance

Covariance and Correlation are very helpful in understanding the relationship between two continuous variables.

Covariance tells whether both variables vary in the same direction (positive covariance) or in the opposite direction (negative covariance).

Covariance(x, y) $Cov(x, y) = \sum_{i=1}^{n} \frac{(x_i - \bar{x})(y_i - \bar{y})}{n-1}$

3.1 Probability Distribution Function

A probability distribution is a mathematical function that describes the probability of different possible outcomes for an experiment. Probability distributions are often depicted using graphs or probability tables.

Probability Distribution Function can be categorized into

• Probability Density Function(PDF)
• Probablity Mass Function(PMF)
• Cumulative Distribution Function(CDF)

While descriptive statistics summarize the characteristics of a data set, inferential statistics help you come to conclusions and make predictions based on your data.

Inferential statistics have two main uses:

• making estimates about populations (for example, the mean SAT score of all 11th graders in the US).
• testing hypotheses to draw conclusions about populations (for example, the relationship between SAT scores and family income).

Percentiles and Quartiles

A percentile is a value below which a certain percentage of observation or data points lies.

Percentiles show how a given value compares to others. The general rule is that if a value is in the kth percentile, it is greater than K per cent of the total values.

Find percentile of n

P = (n/N) * 100

n = Ordinal rank of values
  = No of values below n
N = Total values in the dataset

P% of the entire distribution falls below the value n