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Data Analysis Techniques: Box Plots, Z-Scores, and Probability Simulations

This comprehensive guide covers essential statistical techniques including the 5-number summary, box plots, measures of center (mean and median), and the significance of skewness in data distribution. It further delves into the shape, center, and spread of histograms exemplified by earthquake magnitudes, and explores stem-and-leaf plots for newborn weights. Additionally, it explains z-scores, illustrating their calculation with temperature data and discusses probability through tree diagrams, including concepts of false positives and negative test results in medical diagnostics.

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Data Analysis Techniques: Box Plots, Z-Scores, and Probability Simulations

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Presentation Transcript

  1. Post-Test Prep

  2. #1 The 5-number summary Find the 5-number summary for the data below And create a box plot to display the data

  3. #2 Measures of Center and Outliers Describe the skewness of the box plot you created (skewed left, skewed right, symmetric). How do you know this? If we added the number 305 to the data which measure of center would be more impacted, the mean or the median. Explain.

  4. #3 Shape Center Spread The histogram below displays the magnitude of recorded earthquakes. Describe its shape, center, and spread

  5. #4 Stem and Leaf Plots The stem and leaf plot below displays the weights of newborns at Valley Hospital What is the range of the data above? What is/are the modes? What is the median?

  6. #5 The z-score formula Below are the summary statistics for the temperature in July and October Find the following z-scores • An 80 degree day in July b) A 39 degree day in October • Why was the z-score for the 80 degree day in July positive d) Which would be more unusual, a 61 degree day in October or July?

  7. #6 Simulations A restaurant manager has twelve employees and needs to pick 5 to work a double shift. Their names are listed below. Use the random numbers provided to pick the 5 workers • John 2. Jane 3. Chris 4. Maria • Robin 6. Billy 7. Tim 8. Max • Teri 10. Michelle 11. Jill 12. Christina 05771 20136 05070 98127 83208 71087 21073 42121 76231 01045

  8. #7 Tree Diagrams Build a tree diagram to model the following… 5% of a certain population has a particular disease. 90% of those that have the disease will have a positive result on a diagnostic test. 95% of those that do not have the disease will test negative on a diagnostic test. -What are the chances of a patient having a false positive? -What are the chances of a patient testing negative?

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