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Describing Data Graphically

Common Core Math I Unit 1: One-Variable Statistics Boxplots, Interquartile Range, and Outliers; Choosing Appropriate Measures. Describing Data Graphically. Quantitative Data Dotplot Histogram Boxplot.

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Describing Data Graphically

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  1. Common Core Math I Unit 1: One-Variable StatisticsBoxplots, Interquartile Range, and Outliers; Choosing Appropriate Measures

  2. Describing Data Graphically Quantitative Data • Dotplot • Histogram • Boxplot S-ID.1  Represent data with plots on the real number line (dot plots, histograms, and box plots).

  3. Boxplots – Before we can create we must figure out the “5-number summary” Min Q1 Median Q3 Max Lower Upper Quartile Quartile “median of lower half” “median of upper half”

  4. Create a box plot for the following data:59, 27, 18, 78, 61, 91, 52, 34, 54, 93, 100, 87, 85, 82, 68

  5. Boxplots on the Calculator • Enter the number of buttons • data in List 1 of your calculator. • 2. 2nd y=  Turn boxplot “on” • 3. Window • Xmin= 1 below lowest value • Xmax = 1 larger highest value • Xscl = based on data • If small by 1’s, if large by 10’s, 100’s, etc. • 4. Graph

  6. Boxplots vs. Histograms

  7. Boxplots Min Q1 Median Q3 Max Lower Upper Quartile Quartile The Interquartile Range (IQR) = the spread of the middle 50% of the data. It is represented by the length of the box.

  8. How do you know if a data point is an OUTLIER?

  9. 1.5 IQR rule: Used to identify Outliers!! 1. Calculate the IQR (Range of IQR “Q3-Q1”) 2. Multiply the IQR by 1.5. 3. Add this number to Q3. 4. Any value above this amount is considered an outlier. 5. Then subtract that number from Q1. 6. Any value below this amount is an outlier.

  10. Interpreting Measures of Spread Sensitive to Outliers: • Range: max – min; spread of the entire data set – sensitive to outliers • Standard Deviation: the typical amount that a data value will vary from the mean – sensitive to outliers Not Sensitive to Outliers: • IQR: Q3 – Q1; spread of the middle 50% of the data – not sensitive to outliers

  11. How do you decide whether to use the mean and standard deviation or the median and IQR to summarize the data numerically? Outliers • which are less sensitive to outliers, the median or the mean? Why? • mean and standard deviation are more sensitive because their formulas take every data value into account; • the median and IQR do not, they only look at the “middle” of the data and therefore are not influenced by the presence of outliers

  12. Practice! Below is a stem and leaf plot of the amount of money spent by 25 shoppers at a grocery store. Key: 42 = $42

  13. Practice! – I need to check you off for completion! • Calculate the mean and median. • Calculate the lower and upper quartiles and IQR. • Determine which, if any, values are outliers. • Write several sentences to describe this data set in context. • Name some factors that might account for the extreme values, and the much lower measure of center. Key: 42 = $42

  14. Coming up…

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