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Unit 6: Interpreting Data (Histograms and Measures of Variability…
Unit 6: Interpreting Data
Normal Distributions: Bell Curves
68-95-99.7 rule
68% of the data falls within one standard deviation from the mean
95% of the data falls within two standard deviation from the mean
99.7% of the data falls within three standard deviation from the mean
Z-score: number of standard deviations a data value is above or below the mean
x=M+q(z)
Histograms and Measures of Variability
histograms: Graphs using the frequency and category of certain data
Ideally have 6 categories on the x-axis of the histogram
relative frequency histograms: divide frequency by all of the frequencies added together, and make a histogram
Uniform: looks like block
Normal: bell curve
Bi-Modal: dip in the middle of a bell curve
Skewed (left or right): has a tail toward the direction indicated
Measures of Variability
Range: Max - Min
Standard deviation: average distance each data value is from the mean
Mean: average of all the data points
Min: lowest number
Max: highest number
Quadratic Models
Parabola
Median = y-value of vertex
Find equation given three points
create system of equations by plugging points into general equation
solve using matrices
use the solution to form equation
Correlation and Regression
correlation coefficient: number represented by
r
, where -1≤r≤1 describes how well a data set can be modeled by a line. The closer r is to -1 or 1, the more linear a scatter plot is.
Regression: the process of fitting a line to a data set
Least Squares Regression Line: A linear model that fits a data set (use calculators)
Median-Median Line: used in placed of least squares regression line when the data looks linear but there is an outlier (use calculator)