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Chapters 1 - 4 The Role of Statistics & Graphical Methods for Describing Data

Chapters 1 - 4 The Role of Statistics & Graphical Methods for Describing Data. Statistics. the science of collecting, analyzing, and drawing conclusions from data. Descriptive statistics. the methods of organizing & summarizing data.

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Chapters 1 - 4 The Role of Statistics & Graphical Methods for Describing Data

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  1. Chapters 1 - 4The Role of Statistics&Graphical Methods for Describing Data

  2. Statistics the science of collecting, analyzing, and drawing conclusions from data

  3. Descriptive statistics the methods of organizing & summarizing data If the sample of high school GPAs contained 10,000 numbers, how could the data be described or summarized? • Create a graph • State the range of GPAs • Calculate the average GPA

  4. Inferential statistics involves making generalizations from a sample to a population Based on the sample, if the average GPA for high school graduates was 3.0, what generalization could be made? Be sure to sample from the population of interest!! The average national GPA for this year’s high school graduate is approximately 3.0. Could someone claim that the average GPA for CFBISD graduates is 3.0? No. Generalizations based on the results of a sample can only be made back to the population from which the sample came from.

  5. Variable any characteristic whose value may change from one individual to another Is this a variable . . . The number of wrecks per week at the intersection outside?

  6. Data observations on single variable or simultaneously on two or more variables For this variable . . . The number of wrecks per week at the intersection outside . . . What could observations be?

  7. Types of variables

  8. Categorical variables • or qualitative • identifies basic differentiating characteristics of the population

  9. Numerical variables • or quantitative • observations or measurements take on numerical values • makes sense to average these values • two types - discrete & continuous

  10. Discrete (numerical) • listable set of values • usually counts of items

  11. Continuous (numerical) • data can take on any values in the domain of the variable • usually measurements of something

  12. Classification by the number of variables • Univariate - data that describes a single characteristic of the population • Bivariate - data that describes two characteristics of the population • Multivariate - data that describes more than two characteristics (beyond the scope of this course

  13. the appraised value of homes in Carrollton the color of cars in the teacher’s lot the number of calculators owned by students at your school the zip code of an individual the amount of time it takes students to drive to school Identify the following variables: Discrete numerical Categorical Discrete numerical Categorical Continuous numerical

  14. Graphs for categorical data

  15. Bar Graph • Used for categorical data • Bars do not touch • Categorical variable is typically on the horizontal axis • To describe – comment on which occurred the most often or least often • May make a double bar graph or segmented bar graph for bivariate categorical data sets

  16. Pie (Circle) graph • Used for categorical data • To make: • Proportion 360° • Using a protractor, mark off each part • To describe – comment on which occurred the most often or least often

  17. Graphs for numerical data

  18. Dotplot • Used with numerical data (either discrete or continuous) • Made by putting dots (or X’s) on a number line • Can make comparative dotplots by using the same axis for multiple groups

  19. Types (shapes)of Distributions

  20. Symmetrical • refers to data in which both sides are (more or less) the same when the graph is folded vertically down the middle • bell-shaped is a special type • has a center mound with two sloping tails

  21. Uniform • refers to data in which every class has equal or approximately equal frequency

  22. Skewed (left or right) • refers to data in which one side (tail) is longer than the other side • the direction of skewness is on the side of the longer tail

  23. Bimodal (multi-modal) • refers to data in which two (or more) classes have the largest frequency & are separated by at least one other class

  24. How to describe a numerical, univariate graph

  25. 1. Center • discuss where the middle of the data falls • three types of central tendency • mean, median, & mode

  26. 2. Spread • discuss how spread out the data is • refers to the variability of the data • Range, standard deviation, IQR

  27. 3. Shape • refers to the overall shape of the distribution • symmetrical, uniform, skewed, or bimodal

  28. 4. Unusual occurrences • outliers - value that lies away from the rest of the data • gaps • clusters • anything else unusual

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