There are 2 sets of tools for statistics:

1. Descriptive Statistics: It is used to identify important elements in a dataset and describe the dataset.
2. Inferential Statistics: It explain those relationships via other elements.

            Statistics
     Descriptive     Inferential
Univariate                Hypothesis Testing 
Bivariate                 Model Fitting
Multivariate

Descriptive statistics help us summarize the data.

• It is the first step in exploratory data analysis.
• It helps us understand the data.
• It help you detect outlier.
• Plan to prepare data.
• It also helps us in feature engineering.

          Descriptive
Univariate  Bivariate  Multivariate

Univariate: It involves single variable.

Bivariate: It involves 2 variables, examples: correlation and covariance.

Multivariate: It includes multiple variables, examples: corrilation matrix and covariance matrix.

It is divided into 3 parts:

1. Measures of Frequency

• How often a particular value occur in data.
• It includes frequency tables and histogram.
• A histogram is a visualization where we plot the values, bucketized if needed on the x-axis and on the y-axis we have count of record.

2. Central Tendency

• Measure of central tendency for a variable try to determine one value that best represents your data.
• Common measures include average or the mean of your data, the median value and the mode.

Other measures of central tendency

• Geomatric mean
• Harmonic mean

They are used with ratios or rates

• It is the single best value to represent your data. It not actually be the data point itself.
• It considers every point available in your data.
• It can be computed on discrete data as well as continuous data.

Discrete data can be numeric value that take on values from a predetermine subset such as star ratings.

Continuous data can take on any value in a range.

• It is less influenced by the outlier.
• The median is that value in your data such that 50% of the dataset is either side of it.
• For calculating mean you have to sort the data in ascending or decending order and then use the middle element.
• It the data points are even then average the middle 2.
• The median might be the better measure of central tendency than the mean because it is much more robust to the presence of outliers.
• Like mean, Median does not consider very data point available in the dataset.
• The median can be computed on ordinal data, data that is not numeric but can be sorted like rating like good bad ugly very ugly.

• The value that occurs most frequently in the data, if you plot a histogram, the highest bar represents the mode.

• Examples - casting votes in an election

• It is used with catagorical data, variables that take on a fixed set of values from a predetermined range, examples of catagorical data includes, days of a week, month of the year, makes of cars.

• Mode dont need to be unique.

• Mode is not great for continuous data that can take on any value within the range.

• Contiuous data needs to be descretized before you can perform mode computation.

3. Dispersion

It tells you how your dataset is spread out.

• Range(max-min) of your variable. It is sensitive to outliers. - Range completely ignores the mean, thats why variance comes in.

• Inter Quartile range: Difference between the values at the 75th percentile of your data and the 25th percentile of your data.

• Standard deviation and variance

• Not only tells us how the numbers jumps around but also understands where your numbers are clustered.
• It also considers the mean.
• Variance is the second most important number to summarize your datapoints.
• Variance of the data is simply the sum of the squares of the mean deviations divided by the number of data points you have in your data.

Bessels Correction - put n-1 in the denominator while computing variance