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Statistically Thinking

A study of univariate and bivariate statistics

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Bivariate

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Univariate StatisticsOne variable statistics

• Measures of Central Tendency

• Measures of Variability

• Histogram

• Box-and-Whisker Plot

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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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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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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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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 (Q1,Q2, and Q3) to make the box.

Continued on next slide

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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 (Q3-Q1) 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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Bivariate Statisticstwo variable statistics

• Pearson’s correlation coefficient (r)

• The least squares regression line

• Scatter Plot

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Pearson’s 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 = SSxy/√SSxxSSyy

Pearson’s continued next slide

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Pearson’s 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.

Pearson’s continued next slide

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Pearson’s 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.

• Pearson’s 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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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= SSxy/SSxx and b= y - mx

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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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Resources

• Measures of Central Tendency 1 2• Measures of Variability 1 2• Frequency Distributions and

Histograms 1 2• Box-and-Whisker Plots 1 2• Pearson’s Correlation Coefficient 1 2 • Least Squares Line 1

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Bivariate

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Examples of Project

• Teacher Made

• Student Made