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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
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
```
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