Expected value vs. sample mean

The app to the right will take a sample from a discrete uniform distribution, which includes the numbers 1 through 9, and calculate the sample's mean. You can adjust the size of the sample using the slider. Note that the expected value of this distribution is 5.

A sample is taken, and you win twenty dollars if the sample's mean is less than 4. There's a catch: you get to pick the sample's size.

Which sample size is most likely to win you the twenty dollars?

This exercise is part of the course

Introduction to Statistics in Python

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Introduction to Statistics in Python

IntermediateSkill Level

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Summary statistics gives you the tools you need to boil down massive datasets to reveal the highlights. In this chapter, you'll explore summary statistics including mean, median, and standard deviation, and learn how to accurately interpret them. You'll also develop your critical thinking skills, allowing you to choose the best summary statistics for your data.

Exercise 1: What is statistics?Exercise 2: Descriptive and inferential statistics Exercise 3: Data type classification Exercise 4: Measures of center Exercise 5: Mean and median Exercise 6: Mean vs. median Exercise 7: Measures of spread Exercise 8: Variance and standard deviation Exercise 9: Quartiles, quantiles, and quintiles Exercise 10: Finding outliers using IQR

In this chapter, you'll learn how to generate random samples and measure chance using probability. You'll work with real-world sales data to calculate the probability of a salesperson being successful. Finally, you’ll use the binomial distribution to model events with binary outcomes.

Exercise 1: What are the chances?Exercise 2: With or without replacement?Exercise 3: Calculating probabilities Exercise 4: Sampling deals Exercise 5: Discrete distributions Exercise 6: Creating a probability distribution Exercise 7: Identifying distributions Exercise 8: Expected value vs. sample mean

Current Exercise

Exercise 9: Continuous distributions Exercise 10: Which distribution?Exercise 11: Data back-ups Exercise 12: Simulating wait times Exercise 13: The binomial distribution Exercise 14: Simulating sales deals Exercise 15: Calculating binomial probabilities Exercise 16: How many sales will be won?

It’s time to explore one of the most important probability distributions in statistics, normal distribution. You’ll create histograms to plot normal distributions and gain an understanding of the central limit theorem, before expanding your knowledge of statistical functions by adding the Poisson, exponential, and t-distributions to your repertoire.

Exercise 1: The normal distribution Exercise 2: Distribution of Amir's sales Exercise 3: Probabilities from the normal distribution Exercise 4: Simulating sales under new market conditions Exercise 5: Which market is better?Exercise 6: The central limit theorem Exercise 7: Visualizing sampling distributions Exercise 8: The CLT in action Exercise 9: The mean of means Exercise 10: The Poisson distribution Exercise 11: Identifying lambda Exercise 12: Tracking lead responses Exercise 13: More probability distributions Exercise 14: Distribution dragging and dropping Exercise 15: Modeling time between leads Exercise 16: The t-distribution

In this chapter, you'll learn how to quantify the strength of a linear relationship between two variables, and explore how confounding variables can affect the relationship between two other variables. You'll also see how a study’s design can influence its results, change how the data should be analyzed, and potentially affect the reliability of your conclusions.

Exercise 1: Correlation Exercise 2: Guess the correlation Exercise 3: Relationships between variables Exercise 4: Correlation caveats Exercise 5: What can't correlation measure?Exercise 6: Transforming variables Exercise 7: Does sugar improve happiness?Exercise 8: Confounders Exercise 9: Design of experiments Exercise 10: Study types Exercise 11: Longitudinal vs. cross-sectional studies Exercise 12: Congratulations!