BA 253: Business Statistics 9/7/15

This Week

Chapter 3

ICE 2

·  Return/Discuss ICE 1

·  General questions?

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)

Variability: Sprß------àead 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.

CV = s/xbar*100%

Ex: CV = (s/xbar)*100%. ± $100? Big or small. $1M ± $100, $1000±$100, etc.

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: Do z-scores. z = (x – xbar)/s, SAT – mean = 800, s = 200; ACT – mean = 18, s = 3.

Student 1 / Student 2 / Student 3 / Student 4
Score / SAT 1180 / ACT 20 / ACT 14 / SAT 970
z-score

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