Statistics stands out as a backbone of data science. Whether you are building predictive models, analyzing trends, or making data-driven decisions, a good knowledge of statistics is pretty critical for everything. Statistics helps extract meaningful insights from raw data, verify hypotheses, and model the data for machine learning algorithms, which is used in data science.
This is a crash course for you to cover all the essentials of statistics in data science from descriptive statistics to probability theory, distributions, hypothesis testing, and so much more. By the end of this course, you should be quite well-equipped to apply these concepts to real-world problems and make solid decisions based on your analysis.
Why Statistics?
At its core, data science is about making sense of data. Statistics provides the means to do just that-determine how data are distributed, establish relationships between variables, test hypotheses, or quantify uncertainty to make predictions. For data science, these statistical tools will be crucial for the following uses:
Data Exploration: Summarizing Data and Finding Patterns Using Descriptive Statistics.
Decision Making: Inferential statistics, which allow the prediction and generalization of findings about larger populations through sample data.
Modeling: The creation of statistical models and validation of the constructed models to be able to understand relationships between variables.
Hypothesis Testing: Tests are performed on assumptions present in the data, further leading to conclusions regarding the significance of discovered patterns.
Key Types of Statistics
Statistics can be broadly classified into two categories:
Descriptive Statistics: Describes and summarises data.
Inferential Statistics: Forecasts and makes inferences based on data.
Before we delve into these categories further, let us discuss the basic concepts that serve as an underlying foundation for all statistical techniques.
Descriptive statistics form the first part of data analysis. They provide simple summaries of the sample and the measures. Descriptive statistics help to explain the general characteristics of a dataset without drawing conclusions that are beyond the dataset.
Mean (Arithmetic Average): Sum of all data points divided by the number of data points. It gives an average overall but is susceptible to outliers.
Mean=N∑x
Median: Middle value when data points are ordered in ascending or descending. It is a better measure than the mean in the case of outliers.
Mode: The most frequently occurring value in a dataset. It is useful for categorical data when you want to know the most frequent category.
Range: The difference between maximum and minimum values in a dataset.
Range=Max−Min
Variance: Measures how far each data point in the set is from the mean. Variance is the average of the squared differences from the Mean.
Variance(σ2)=N∑(x−μ)2
Standard Deviation: The square root of the variance. It provides a measure of the typical distance of values from the mean.
Standard Deviation(σ)=N∑(x−μ)2
Interquartile Range (IQR): Measures the difference between 75th percentile (Q3) and 25th percentile (Q1)
IQR=Q3−Q1
Skewness
Skewness: This is a measure of the asymmetry of the distribution of data. A skewed dataset means your data is not symmetrically distributed.
Positive Skew: Tail on the right.
Negative Skew: Tail on the left.
Kurtosis
Kurtosis: This measures the “tailedness” of the data distribution.
High Kurtosis: Data has heavy tails (outliers).
Flat Kurtosis: Data have light tails (few outliers).
Histograms: It is a graphical representation of the distribution of a data set.
Box Plots: It is used to represent the five-number summary of a data set.
Minimum, First Quartile, Median, Third Quartile, Maximum.
Bar Charts: Graphical presentation of categorical data.
Scatter Plots: Plotting the relationship between two variables.
Understanding probability is quite fundamental in data science because this essentially defines prediction. Probability is the quantification of uncertainty, which enables one to make decisions about the data when the outcome is not certain.
P(A)=Total number of outcomes/Number of favorable outcomes
P(Not A)=1−P(A)
P(A∩B)=P(A)×P(B)
Conditional probability is the probability of an event occurring given that another event has already occurred. This concept is critical in understanding the relationships between variables.
P(A∣B)=P(A∩B)P(B)P(A|B) = \frac{P(A \cap B)}{P(B)}P(A∣B)=P(B)P(A∩B)
Bayes’ Theorem is a way to find a probability when we know certain other probabilities. It’s particularly useful in machine learning for classification problems.
P(A∣B)=P(B)P(B∣A)×P(A)
The normal distribution, also known as the Gaussian distribution, is the most important distribution in statistics. Many real-world phenomena follow a normal distribution. The normal distribution is symmetric and bell-shaped.
Properties:
Inferential statistics allows you to make predictions or inferences about a population based on a sample of data.
Hypothesis testing helps to determine whether there is enough evidence to infer that a certain condition is true for the entire population.
Steps in hypothesis testing:
The p-value is the probability that the observed data occurred by chance. A low p-value (typically < 0.05) indicates strong evidence against the null hypothesis.
A confidence interval gives a range of values within which you expect the population parameter to fall.
Correlation measures the strength and direction of the relationship between two variables. A positive correlation means the variables move in the same direction, while a negative correlation means they move in opposite directions.
Linear regression is a method to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to the observed data.
Role of Statistics in Data Science
It is so important for any data scientist to master the basics on statistics. Knowing how to understand the distributions, hypothesis testing, and model building forms the foundation from which data science decisions are made. These basic statistical concepts placed in usage will put you in the driving seat for analyzing data, making predictions, and driving insights to make an impact in the real world.
Given how important data-driven decisions are in your field, the power of statistics really cannot be overstated. As you continue on your journey in data science, these statistical tools will be just as much part of your natural toolbox as the ability to uncover patterns, answer questions, and solve complex problems in a meaningful way.
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