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What is Probability and Statistics?
Probability and Statistics usually refers to an introductory course in probability and statistics.
The “probability” part of the class includes calculating probabilities for events happening. While it’s usual for the class to include basic scenarios like playing cards and dice rolling at first, these basic tools are used later in the class to find more complex probabilities, like the probability of contracting a certain disease.
The “statistics” part of probability and statistics includes a wide variety of methods to find actual statistics, which are numbers you can use to generalize about a population.
Statistics How To example: you could calculate the height of all your male classmates and find the mean height to be 5’9″ — this is a statistic. But then you could take that statistic and say “I think the average height of an American male is 5’9″ “. How accurate your guess is depends on many factors, including how many men you measured and how many men are in the entire population. Statistics are useful because we often don’t have the resources to measure, survey or poll every member of a population, so instead we take a sample (a small amount).
What is Calculus Based Statistics?
Calculus Based statistics takes the four core concepts of calculus (Continuity, Limits, Definite integral, Derivative) and applies them to statistical theory. Essentially, non-calculus based statistics is for consumers of statistics and calculus based statistics is more suited for people who want to create statistics (Columbia, 2021).
Elementary Statistics vs. Calculus Based Statistics
There are many similarities and some important differences between Elementary Statistics and Calculus Based Statistics. Whichever class you take, you’re going to cover the same core concepts including ANOVA, Confidence intervals, Correlation, Regression and Statistical Inference.
The main difference is in how these topics are approached. For example, in a basic stats class, confidence intervals are introduced as a way to describe the distribution of parameters (i.e. how spread out your estimated results are). The focus is on how to make and interpret these intervals. With a calculus based statistics approach, functions are derived for these intervals.