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BA 253: Business Statistics Today Chapter 3 05/05/15 Wednesday More Ch 3 General questions. Chapter 2 (Descriptive Tables and Graphs) Qualitative (pp. 25-28) versus Quantitative Data: How many minutes to commute to class? o Frequency o Relative Frequency o Histogram (5-10 classes, choose 6, not RS) o Class Width = (Biggest – Smallest)/Number of Classes o Stem-and-Leaf o Mean, Median, Mode By hand. Calculator o Do on Excel? Collect Textbook (or other) Data Chapter 3: Numerical Descriptive Statistics Location = “middle” = mean, median, mode (plus a few others) Variability = “spread” = range, sample standard deviation, variance Mean = Median = Mode= Percentiles (pp. 81 – 82) i = (p/100)*nth data point Q1 = point where 25% of data are smaller Q3 = point where 75% of data are smaller Now, do all on TI-83 (Stats, Edit, Calc, OneVar) or Excel Variability: Spr-------------ead of the data. Range, IQR: (page 84) Sample Variance = s2 = sum ( )2/(n-1) Sample SD = s = sqrt(s2) CV = s/xbar*100% Do for data, on TI 83 Note: Often, mean ± s is all you need to know. Central Tendency = mean, median = “middle” of the data Variability = standard deviation Finish Ex: Three investments, A, B or C. Which would you prefer? Roll die. A: all $14,000; B: 0, 10, 15, 15, 20, 30, C: -50, -10, 15, 15, 40, 80 xbar = median. Calculate s, CV for each. Ex: CV = (s/xbar)*100%. ± $100? Big or small. $1M ± $100, $1000±$100, etc. Ex: Empirical rule on basic data. Ex: Textbook data: Mean, Median, Standard Deviation??? CV = (s/xbar)*100% Do textbook. Do Five Number Summary (5#s) for Textbook/ compare to x ± s. Do Empirical Rule for Textbook. Ex: Do z-scores. z = (x – xbar)/s, SAT – mean = 800, s = 200; ACT – mean = 18, s = 3. Score z-score Student 1 SAT 1180 Student 2 ACT 20 Student 3 ACT 14 When is a point an outlier? Depends on n, distance from middle, others? No exact rule. Consider |z-score| > 2.5 or 3? Factor in s which affects z. Do Tukey’s method: o IQR = Q3 – Q1 o Find (Q1 – 1.5 IQR, Q3 + 1.5 IQR), outliers outside. o Data: 10, 20, 30, 40, 50, 100 Student 4 SAT 970