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Rubric Unit Plan Univariate Bivariate Examples Resources Curriculum Statistically Thinking A study of univariate and bivariate statistics

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Rubric Unit Plan Univariate Bivariate Examples Resources Curriculum Univariate Statistics One variable statistics Measures of Central Tendency Measures of Variability Histogram Box-and-Whisker Plot

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Rubric Unit Plan Univariate Bivariate Examples Resources Curriculum Measures of Central Tendency Mean – The mean of a set of data is the average of the data. Median – The median of a set of data is the middle number or the average of the two middle numbers of a set of data. Mode – The mode of a set of data is the number or numbers that are most repeated.

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Rubric Unit Plan Univariate Bivariate Examples Resources Curriculum Measures of Variability Range – The difference of the largest and the smallest items in a set a data. Mean Deviation – The average deviation from the mean. Variance – The average of the deviations from the mean squared. Standard Deviation – The square root of the variance (σ)

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Rubric Unit Plan Univariate Bivariate Examples Resources Curriculum Histogram A histogram is a bar chart formed from a frequency distribution of a set of data. Frequency distributions are made up of uniform classes which incorporate all of the data.

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Rubric Unit Plan Univariate Bivariate Examples Resources Curriculum Box-and-Whisker Plot A box-and-whisker plot is a good way to show the variability of data. A box-and-whisker plot uses quartile points (Q 1,Q 2, and Q 3 ) to make the box. Continued on next slide

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Rubric Unit Plan Univariate Bivariate Examples Resources Curriculum Box-and-Whisker Plot The whiskers are drawn to the maximum and minimum unless those points are more than 1.5 times the interquartile range (Q 3 -Q 1 ) from their respective quartile point. Points outside this range are called outliers and are represented with a point. Whiskers are drawn to the largest or smallest value that is not an outlier.

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Rubric Unit Plan Univariate Bivariate Examples Resources Curriculum Bivariate Statistics two variable statistics Pearsons correlation coefficient (r)Pearsons correlation coefficient (r) The least squares regression line Scatter Plot

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Rubric Unit Plan Univariate Bivariate Examples Resources Curriculum Pearsons Correlation Coefficient (r) The Pearson correlation coefficient shows how well two quantitative sets of data are linearly correlated. The value of r is calculated by using the formula r = SS xy /SS xx SS yy Pearsons continued next slide

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Rubric Unit Plan Univariate Bivariate Examples Resources Curriculum Pearsons Correlation Coefficient (r) The value of r will always be between - 1 and 1. With -1 being a perfect indirect linear relationship and 1 being a perfect direct relationship. If r is between -.25 and.25, then there is no linear correlation. If r is between -.25 and -.5 or.25 and.5, then there is a weak correlation. Pearsons continued next slide

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Rubric Unit Plan Univariate Bivariate Examples Resources Curriculum Pearsons Correlation Coefficient If r is between -.5 and -.75 or.5 and.75, then there is a moderate correlation. If r is between -.75 and -1 or.75 and 1, then there is a strong correlation. Pearsons only shows linear correlations; if your r value is outside the range given, then check your work you probably did something wrong.

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Rubric Unit Plan Univariate Bivariate Examples Resources Curriculum Least Squares Line The least squares line is an algebraic method of finding the line of best fit for a set of linearly correlated data. The formula for the least squares line can be written as follows: y=mx+b where m= SS xy /SS xx and b= y - mx

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Rubric Unit Plan Univariate Bivariate Examples Resources Curriculum Scatter Plot A scatter plot is a visual representation of bivariate data shown by plotting each data item on the x, y coordinate plane.

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Rubric Unit Plan Univariate Bivariate Examples Resources Curriculum Resources Measures of Central Tendency 1 212 Measures of Variability 1 212 Frequency Distributions and Histograms 1 212 Box-and-Whisker Plots 1 212 Pearsons Correlation Coefficient 1 212 Least Squares Line 11

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Rubric Unit Plan Univariate Bivariate Examples Resources Curriculum Examples of Project Teacher Made Student Made

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Unit 4 – Probability and Statistics

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