AP Statistics: Chapter 2 (2.1 + 2.2)

Transformations—> Adding + Subtracting

Adds a to measures of center (mean, median, quartiles, percentiles, min/max) but does not change the shape (range, iqr, standard deviation)

Example of Adding + Subtracting

error = guess - 13

mean - 13= x

SD = SD

min - 13 = x

Q1 - 13 = x

med - 13 = x

Q3 - 13 = x

max - 13 = x

IQR = IQR

Range = Range

Transformations - Multiplying + Dividing

Affects everything!

Multiplies (divides) measures of center, measures of spread

Does not change shape of distribution

In 2010, taxi cabs in New York City charged an inital fee of 2.50 plus 2 per mile. In equation form, fare = 2.50 + 2m.

At the end of a month, a businessman collects all his taxi cab receipts and calculates some numerical summaries. The mean fare he paid was 15.45 with a SD of 10.20. What are the mean and SD of the lengths of his cab rides in miles?

Mean:

15.45 = 2.5 + 2m —> 15.45-2.5 divided by 2 = 6.475 miles

SD

Just 10.20/2 because SD is not added or subtracted—> 5.1 miles

Percentile

pth percentile is the value with p% of observations less than or equal to it

When it asks to interpret the difference between percents..

find the difference between percents and thats how much percent the x had

Z-scores or standardizing score

How many standard deviations above the mean an observation falls (x-mean)/SD

Example of Z-score: Jenny scored a 86 on her test, and the class mean is a 80 and the SD is a 6.07. What is her z-score?

86-80 = 6/6.07—> 0.99—> 0.99 SDs above the class mean