Effortlessly Using the Normal Cumulative Distribution Function in Python
Introduction to Statistics in Python Course Outline
Summary Statistics
- In this chapter, you’ll explore summary statistics including mean, median, and standard deviation.
- Learn how to accurately interpret summary statistics.
- Develop critical thinking skills to choose the best summary statistics for your data.
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Random Numbers and Probability
- Learn how to generate random samples and measure chance using probability.
- Work with real-world sales data to calculate the probability of a salesperson being successful.
- Use the binomial distribution to model events with binary outcomes.
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More Distributions and the Central Limit Theorem
- Explore the normal distribution, one of the most important probability distributions in statistics.
- Create histograms to plot normal distributions.
- Gain an understanding of the central limit theorem.
- Expand your knowledge of statistical functions by adding the Poisson, exponential, and t-distributions to your repertoire.
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Distribution of Amir’s Sales
To understand the distribution of Amir’s sales, we can utilize the normal distribution. Here’s a sample code in Python to plot a histogram of Amir’s sales data:
Probabilities from the Normal Distribution
To calculate probabilities from the normal distribution, we can use the norm
function from the scipy.stats
module. The following code demonstrates how to calculate the probability of sales falling within a certain range:
Simulating Sales under New Market Conditions
If you want to simulate sales under new market conditions, you can use the norm.rvs
function to generate a random sample from a normal distribution. Here’s an example code snippet:
The Central Limit Theorem
The central limit theorem states that the sampling distribution of the mean approaches a normal distribution as the sample size increases. To visualize sampling distributions, you can use the following code:
The Mean of Means
The mean of means refers to the fact that the average of sample means is equal to the population mean. Here’s a code snippet to demonstrate this:
The Poisson Distribution
The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space. To identify the lambda parameter for a Poisson distribution, you can use the following code:
Tracking Lead Responses
To track lead responses, you can use the exponential distribution. The following code snippet demonstrates how to generate random lead response times:
More Probability Distributions
In addition to the normal and Poisson distributions, there are many other probability distributions available in Python. Some examples include the exponential distribution, gamma distribution, and beta distribution.
The t-Distribution
The t-distribution is used when the sample size is small or the population standard deviation is unknown. To utilize the t-distribution, you can use the t
function from the scipy.stats
module. Here’s an example code snippet:
Correlation and Experimental Design
In this chapter, you’ll learn how to quantify the strength of a linear relationship between two variables. You’ll also explore how confounding variables can affect the relationship between two other variables. Furthermore, you’ll understand how a study’s design can influence its results and potentially affect the reliability of your conclusions.
Note: This article is a summary of the Python Learn course on Introduction to Statistics. The examples and code snippets are intended to help learners understand the concepts and apply them in Python programming.