Transcript Slide 1
CHAPTER 2 Data Description “The Collection, Display, and Summary of Data” Chapter 2 Summary By Chris Schulze Gonick: The Cartoon Guide To Statistics (Chapter 2) CHAPTER 2 - DATA DESCRIPTION In Chapter 2 we discuss describing data by using measures: From the center, The spread, By making visual representations of the data set. Gonick: The Cartoon Guide To Statistics (Chapter 2) METHODS TO DISPLAY DATA Dot Plot Frequency Table Histogram Stem-and-Leaf Gonick: The Cartoon Guide To Statistics (Chapter 2) Stem 8 9 10 11 Leaf 1456 347 023 05 FREQUENCY TABLE A table that lists items and uses tally marks to record and show the number of times they occur. Dot Plot Is a statistical chart consisting of group of data points plotted on a simple scale. Used for continuous, quantitative, univariate data. Suitable for small or moderate sized data sets. Gonick: The Cartoon Guide To Statistics (Chapter 2) H ISTOGRAM A graphical display of tabulated frequencies, shown as bars. Shows what proportion of cases fall into each of several categories •Each bar covers an interval •The bar height is the number of data points Relative Frequency Histogram •Plots Relative Frequency against the Weight •Same as the Histogram o Except for the vertical scale Gonick: The Cartoon Guide To Statistics (Chapter 2) STEM-AND-LEAF Used to analyze large amounts of numbers. Two columns Data is arranged by place value Stem – The digits in the largest place Leaf – The digits in the smallest place Shows trends or Bias Easy to use Compact arrangement Stem Leaf 8 1456 9 347 10 023 11 05 Gonick: The Cartoon Guide To Statistics (Chapter 2) MEASURES OF THE CENTER Values at the middle or center of a data set. The Mean The average value of your data set Obtained by adding all the data and dividing by the number of observations The Median Not sensitive to extreme values It is the middle value of you data set 1 1 1 2 2 3 4 Mean = 42/13 = 3.23 4 4 4 5 Median = 4 Gonick: The Cartoon Guide To Statistics (Chapter 2) 5 6 MEASURES OF SPREAD Tells us how much a data sample is spread out or scattered Histogram Box and Whiskers InterQuartile Range (IQR) Outliers Standard Deviation Variance Gonick: The Cartoon Guide To Statistics (Chapter 2) BOX AND WHISKERS (BOX PLOT) InterQuartile Range (IQR) The middle 50 It is equal to the difference between the 3rd and 1st quartiles. Outliers an observation that is numerically distant from the rest of the data. * Outliers Lowest Value (MIN) Lower Quartile (Q1) Median (Q2) Upper Quartile (Q3) Highest Value (MAX) Interquartile Range Q3 - Q1 Range MAX - MIN Gonick: The Cartoon Guide To Statistics (Chapter 2) * STANDARD DEVIATION Helps to measure how “spread out” a distribution is. Standard Deviation (S) = The average distance from the Mean (using squares). It is also the square root of the variance. Where: X = list of numbers N = How many number are in the list ∑ = Sum of the numbers x = Mean S = Standard Deviation Gonick: The Cartoon Guide To Statistics (Chapter 2) Z – SCORES Z-Score (or standard score) indicates how many standard deviations an observation or datum is above or below the mean. Z – Score = The distance from the mean per standard deviation. Where: X = Raw Score to be standardized x = Mean S = Standard Deviation Gonick: The Cartoon Guide To Statistics (Chapter 2) EMPIRICAL RULE (68-95-99.7) If data distribution is approximately normal then 68% of the values are within 1 standard deviation of the mean, 95% of the values are within two standard deviations, and 99.7% are within 3 standard deviations. Specifically applies to a normal bell-shaped distribution Frequently applied to any mounded distribution Gonick: The Cartoon Guide To Statistics (Chapter 2) KEY TERMS TO REMEMBER Frequency Histogram Stem-and-leaf diagram Mean Median Interquartile Range (IQR) Box plot Box and whiskers plot Variance Standard deviation Z-score Outlier Gonick: The Cartoon Guide To Statistics (Chapter 2) Helpful Websites http://www.dimensionresearch.com/index.html http://stattrek.com http://easycalculation.com/statistics http://www.tutorvista.com REFERENCES http://jalt.org/test/str_2.htm, Shiken: JALT Testing & Evaluation SIG Newsletter http://www.wikipedia.org/ http://www.khanacademy.org/ The Cartoon Guide to Statistics, Gonick, 1993 An Introduction to Statistical Problem Solving in Geography, McGrew, 1993 Gonick: The Cartoon Guide To Statistics (Chapter 2)