AP Statistics Unit 2

Z-Score: # of _____ above or below the _____.

Formula: ____

standard deviations, mean

pth percentile: The value with p percent of the observations____ to it

less than or equal

Calculating percentile from value

Calculating value from percentile

Find place in line, then divide by total

Multiply by total to get place in line, then find value

Standardization: a point’s location in the distribution depends on both ____ and _____

distance from center, spread/variation

why isn't the maximum act score of 36 at the 100th percentile

Because the 100th percentile means that your ACT scorewas higher than everyone else's. However, the highest score is 36, but many people can score 36 and they would be tied.

Density curve characteristics:

• _____ data

• total area = ____

• used to calculate ____

quantitiative

1

probability

Where do you find median in density curve?

Where do you find mean in density curve?

splits area in half

balance point (pulled toward tail)

If data is symmetric, what is the relationship btwn mean and median

=

What is the shape of a Normal Curve?

____modal and ______ (no/few _____)

____ shaped

unimodal, symmetric, outliers

bell

What two numbers do we use to describe a Normal Distribution?

μ = population mean

σ = standard deviation

Empirical Rule

68-95-99.7

68% of data is within 1 standard deviation from mean

95% of data is within 2 standard deviations from mean

99.7% of data is within 3 standard deviations from mean

Relating Normal distribution to x-axis values, z-score, and percentile

Start in the middle: mean, 0, 50

As you go out, as z score increases by 1, %tile increases by ½ empirical rule, and value increases by 1 standard deviation

Standard Normal Distribution

N(0,1)

Normality can be assessed using closeness to empirical rule or normal probability plot

If data is normal, what should normal probability plot look like?

if skewed left:

if skewed right:

follow the line y=x, data clustered in middle

data clustered on right

data clustered on left

z scores of Q1 and Q3

standard deviations in IQR

-0.674, 0.674,

1.349