University:
Eastern Kentucky University
Course:
STA 215 | Introduction to Statistical Reasoning
Academic year:

2020
Views:

244

Pages:

1
Author:

Isabella Bolton

Physics and Math 12: Data-Based and Statistical Reasoning Measures of Central Tendency Probability Provide a single value representation for the middle of the data set. Mean: The average. Median: The value that lies in the middle of the data set. Tends to be least susceptible to outliers, but may not be useful for data sets with large ranges. Mode: The data point that appears most often. Independent The probability of independent events does not change Events: based on the outcomes of other events. Dependent The probability of a dependent event changes depending on Events: the outcomes of other events. Terminology: Mutually Exclusive: Cannot occur simultaneously. When a set of outcomes is exhaustive, there are no other possible outcomes. Distributions Statistical Testing Normal Symmetrical and the mean, median, and mode are equal. Distribution: Hypothesis Use a known distribution to determine whether the null Tests: hypothesis can be rejected. p-value: Whether or not a finding is statistically significant is determined by the comparison of a p-value to the selected significance level (a ). A significance level of 0.05 is commonly used. Confidence Are a range of values about a sample mean that are used Intervals: to estimate the population mean. A wider interval is associated with a higher confidence level (95% is common). Standard Distribution: A normal distribution with a mean of 0 and a standard deviation of 1. It is used for most calculations. Hypothesis Testing Chart with Type 1 and Type 2 Errors Skewed Have differences in their mean, median, and mode. Skew Distribution: direction is the direction of the tail. Mode Median Mode Median Mean Mean LEFT skewed (negative skewedness) RIGHT Skewed (positive skewedness) Bimodal Multiple peaks, although not necessarily multiple modes. Distribution: Measures of Distribution Range: Difference between largest and smallest value. Interquartile The difference between the value of the third quartile and Range: first quartile. Can be used to determine outliers. Standard A measurement of variability about the mean. Can be used Deviation ( s ): to determine outliers. Charts, Graphs, and Tables Pie and Bar Charts: Used to compare categorical data. Histograms and Box Plots: Used to compare numerical data. Linear, Semilog, and Log-log Plots: Can be distinguished by the axes. Outliers: In general, any value that lies more than 3 standard deviations from the mean. Exponential Relationship Logarithmic Relationship Slope: Quadratic Relationship !"#$ !%& Curvilinear Relationship

Physics and Math 12 Data-Based and Statistical Reasoning

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