Sample mean vs. Theoretical mean

The app will take a sample from a discrete uniform distribution, which includes the numbers one through nine, 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 five.

A sample is taken, and you win twenty dollars if the sample's mean is less than four. 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

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Introduction to Statistics

BeginnerSkill Level

4.8+

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Summary statistics gives you the tools you need to describe your data. 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: Using statistics in the real-world Exercise 3: Identifying data types Exercise 4: Descriptive vs. Inferential statistics Exercise 5: Measures of center Exercise 6: Typical number of robberies per London Borough Exercise 7: Choosing a measure Exercise 8: London Boroughs with most frequent crimes Exercise 9: Measures of spread Exercise 10: Defining measures of spread Exercise 11: Box plots for measuring spread Exercise 12: Which crime has the larger standard deviation

Probability underpins a large part of statistics, where it is used to calculate the chance of events occurring. You'll work with real-world sales data and learn how data with different values can be interpreted as a probability distribution. You'll find out about discrete and continuous probability distributions, including the discovery of the normal distribution and how it occurs frequently in natural events!

Exercise 1: What are the chances?Exercise 2: What is more likely?Exercise 3: Chances of the next sale being more than the mean Exercise 4: Conditional probability Exercise 5: Dependent vs. Independent events Exercise 6: Orders of more than 10 basket products Exercise 7: Discrete distributions Exercise 8: Identifying distributions Exercise 9: Sample mean vs. Theoretical mean

Current Exercise

Exercise 10: Continuous distributions Exercise 11: Discrete vs. Continuous distributions Exercise 12: Finding the normal distribution Exercise 13: Probability with a uniform distribution

It's time to explore more probability distributions. You'll learn about the binomial distribution for visualizing the probability of binary outcomes, and one of the most important distributions in statistics, the normal distribution. You'll see how distributions can be described by their shape, along with discovering the Poisson distribution and its role in calculating the probabilities of events occuring over time. You'll also gain an understanding of the central limit theorem!

Exercise 1: The binomial distribution Exercise 2: Recognizing a binomial distribution Exercise 3: How probability affects the binomial distribution Exercise 4: Identifying n and p Exercise 5: The normal distribution Exercise 6: Recognizing the normal distribution Exercise 7: What makes the normal distribution special?Exercise 8: Identifying skewness Exercise 9: Describing distributions using kurtosis Exercise 10: The central limit theorem Exercise 11: Visualizing sampling distributions Exercise 12: The CLT vs. The law of large numbers Exercise 13: When to use the central limit theorem Exercise 14: The Poisson distribution Exercise 15: Identifying Poisson processes Exercise 16: Recognizing lambda in the Poisson distribution

In the final chapter, you'll be introduced to hypothesis testing and how it can be used to accurately draw conclusions about a population. You'll discover correlation and how it can be used to quantify a linear relationship between two variables. You'll find out about experimental design techniques such as randomization and blinding. You'll also learn about concepts used to minimize the risk of drawing the wrong conclusion about the results of hypothesis tests!

Exercise 1: Hypothesis testing Exercise 2: Sunshine and sleep Exercise 3: The hypothesis testing workflow Exercise 4: Independent and dependent variables Exercise 5: Experiments Exercise 6: Recognizing controlled trials Exercise 7: Why use randomization?Exercise 8: Correlation Exercise 9: Identifying correlation between variables Exercise 10: What can correlation tell you?Exercise 11: Confounding variables Exercise 12: Interpreting hypothesis test results Exercise 13: Significance levels vs. p-values Exercise 14: Type I and type II errors Exercise 15: Congratulations!