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

2. 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

3. 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.

4. 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)

5. 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.

6. 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

7. 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.

8. 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

9. 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

10. 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

11. 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.

12. 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

13. 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.

14. 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

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