2.1 Box plots
- 5 number summary (min, Q1, median, Q3, max)
- Interquartile range (1.5*IQR rule – “fences”)
- Ex. 2, 5, 6, 7, 9, 9, 16
- median: 7, Q1: 5, Q3:9, min: 2, max: 16
- IQR: Q3 – Q1. 9 – 5 = 4.
- 1.5*IQR: 4*1.5 = 6
- fences: Q1 – 1.5*IQR, Q3 + 1.5*IQR. 5-6 = -1, 9+6 = 15. Fences: -1, 15
- 16 is an outlier.
- mean, median, mode
2.2 Measures of Spread
- Standard Deviation
- Ex:
- Data: 41, 55, 48, 44
- mean = 47, n = 4
- Deviations: -6, 8, -3, 1
- Deviations squared: 36, 64, 9, 1
- sum: 110, divide by (n-1), 110/3 = 36.6666667
- square root: 6.0553
- standard deviation: Acceptable “average” amount of error
- DOES NOT show outliers.
2.3 Histograms and percentile ranks
- Histograms: bin widths, frequency
- percentile rank: (# of data points that you are higher than)/(total number of data points)
- You are 5 ft 8 inches. You are taller than 12 kids on your basketball team. Including you, there
are 20 kids on the basketball team, what is your percentile rank? 60th percentile.
- You score a 32 out of 35 on your test. 2 other kids also scored a 32 out of 35. Only 3 kids have
a better score than you. There are 33 kids in your class. What is your percentile rank?
27/33=82nd percentile
- You take your driving test. You score 80 out of 100 and pass. 500 kids took the test this
month. 150 kids scored better than you, and 50 other kids tied you. What is your percentile
rank? 299/500= .598=60th percentile
11.2 Probability Distribution
- probability graphs have area of 1 or 100%
- Probability of:
- less than, more than, or between 2 values.
- by finding the area, or by counting squares and divide by total
- mode (highest point on graph, or no mode) and median (splits the area into 2 equal pieces)
11.3 Normal Distribution Curve
- bell shaped
- 68% (within one standard deviation of the mean)-95% (within 2 standard deviations)-99.7% (within 3
standard deviations)
- point of inflection is at one standard deviation away from the mean
- mean = mu, standard deviation = sigma.
11.4 z-scores/ confidence intervals
- z= (x – mean)/(standard deviation)
- z tells you how many standard deviations you are from the mean.
- confidence intervals for 68%, 95%, 99.7%