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Chapter 1 Review: Exploring Data

Chapter 1 Review: Exploring Data. Group Members: Charlie, Tyler, Renzheng. Model of the Big Bang. The Big Idea. Analyze data by using graphs and numerical summaries Use graphs to display categorical or quantitative data

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Chapter 1 Review: Exploring Data

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  1. Chapter 1 Review:Exploring Data Group Members: Charlie, Tyler, Renzheng

  2. Model of the Big Bang The Big Idea • Analyze data by using graphs and numerical summaries • Use graphs to display categorical or quantitative data • Describe the overall pattern by interpreting shape, center, spread, and outliers (SOCS) • Choose a which center and summary best fits the data. (mean and deviation or five-number summary) • Determine the effect of a linear transformation on center and spread

  3. Vocabulary You Need to Know • Individuals – are the objects described by the data. Can be people or things • Variables – are any characteristics of an individual • Categorical variables - places an individuals into groups or categories • Quantitative variables – takes numerical values like 2 or 4.5 • Distribution – of a variable tells us what values the variable takes and how often it takes these values

  4. Key Topics Covered in this Chapter • Graph categorical data on pie charts and bar graphs. Graph quantitative data on stemplotsand histograms, • Ogive or relative cumulative frequency graphs and timeplots are quantitative • Describe Shape: symmetric or skewed, unimodalor no modes • Describe Center: Mean or Medium. They are the same in symmetric but in a skewed, the mean is farther out than the median near the tail • Describe Spread: range, quartiles, five number summary, standard deviation • Outliers: Median and quartiles are resistant. Mean and Std deviations arnt

  5. Formulas You Should Know • Mean • Variance • Standard Deviation • Outliers smaller than Q1 – (1.5 *IQR) or larger than Q3 – (1.5*IQR) • Linear transformation xnew = a + bx (a shifts values up or down, b changes the size) • Five number summary (min, Q1, medium, Q3, max) • Range = maximum – minimum

  6. Calculator Key Strokes • Enter data into L1 and L2 then press 1-var stat under calculations. • This will find the mean and standard deviations. • Remember the difference between (s) sample and (σ) population

  7. Helpful Hints • Use back to back stemplots and side by side boxplots are used to compare quantitative distributions • Use mean and standard deviation for symmetric and Normal distributions and the five number summary for skewed distributions • The sum of all deviations from their mean will always be 0. s = 0 only when all observations have the same value • The number n – 1 is called the degrees of freedom of the variance or std. deviation • Average value refers to the mean and typical value to the medium • Histograms should always have bins of the same size and the bars touch each other

  8. Example Problem(s) • -799, 0, 4, 32, 54 ,93, 354, 354, 1534, 3942, 4032, 5030 • Find the Five number summary • Find any outliers • Find the mean and standard deviation • Make a boxplotand a histogram • Describe SOCS • a) (-799, 43, 86, 2738, 5030) • b) None • c) Mean = 1219.1666 std dev. = 1965.9759 • d) • e) Skewed, no outliers, medium, quartiles

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