AP Final Exam Flashcards by Olivia Brown

SOCS - fairly symmetric

Shape
Center- mean
Spread - SD
Outliers - too small if Q1 - 1.5
too big is Q1 + 1.5

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SOCS - slightly/strongly skewed

Shape
Center - median
Median - IQR
Outliers - too small if Q1 - 1.5
too big is Q1 + 1.5

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How to find SOCS easily

Make list –> stats –> stat calc –> 1 variable stats

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True or false: you can determine the shape with a boxplot

False

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Interpret SD

The (context) typically varies by (SD) from the mean of (mean).

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Interpret percentile

(Percentile) % of (context) are less than or equal to (value).

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Interpret z-score

(Specific value w/ context) is (z-score) standard deviations (above/below) the mean.

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Describing the distribution

DUFS:
- Direction - (+) or (-)
- Unusual features - outliers or clusters
- Form - linear or nonlinear
- Strength - weak, moderate, or strong

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Calculate slope

use b in y(hat) = a + bx –> b/increment (ex. years)

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Interpret slope

The predicted (y-context) (increases/decreases) by (slope) for each additional (x-context).

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Interpret coefficient of determination (r^2)

(r^2 as percentage) of the variation in (y-context) can be explained by the linear relationship with (x-context).

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Calculate residual (r)

r = (actual) - (predicted)
predicted = y(hat) = a + bx

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Interpret residual (r)

The actual (y-context) was (r) less/greater than the predicted (y-context & predicted value).

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Convenience sample

Selected for inclusion because they are easy to access
(ex. first 30 people to walk through the door)
- Underestimates or overestimates true proportion
- Not representative of population

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Voluntary response

Choose to participate in a survey or experiment

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Simple random sample

Random sample which takes a random population and randomly assigns them into groups with equal probability.

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Stratified sampling

Takes population and splits them into groups (strata) into a characteristic that we think has some effect.
(ex. SRS within grades)
- Homogeneous groups
- SRS within each group

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Cluster sample

Grouping is similar to population and SRS is taken to choose a cluster.
(ex. SRS of classrooms)
- Heterogeneous groups
- SRS of groups

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Undercoverage bias

Don’t have access to survey

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Response bias

No reply

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Response bias

Participants who are untruthful

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Confounding variable

Variable that causes suspicious association

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Observational study

Variables are observed to determine if there’s a correlation

Experimental study

Using controlled variables to determine if there’s causation

Use blocking for...

Experimental designs

Use stratifying and clustering for...

Observational studies

Mutually exclusive

Probability for A or B (A U B); cannot occur together - think ADDITION - If there's an overlap, subtract

Independent

Probability A and B; one thing does not affect the other - think MULTIPLY - If A already happened; what's the probability of second

How to find probability when given percentages

Tree diagram

Interpret probability (A) (mutually exclusive)

After many, many (context), the proportion of times that (context A) will occur is about (P(A)).

Describing binomial distribution

Conditions: BINS 1) Binary - success or failure 2) Independent 3) Number of trials fixed - n = ___ 4) Same probability - p = ___ - Shape - (np ≥ 10, n(1-p) ≥ 10) - Center - mean: μx = np - Variance - SD: ox = √np(1-p)

Calculate binomial probability (exactly)

binompdf (clearly identify parameters)

Calculate binomial (a least)

1 - binompdf (clearly identify parameters)

Interpret conditional probability (independence)

Given (context B), there is a P(A|B) probability of (context A)

Interpret expected value (mean, μ)

If the random process of (context) is repeated many times, the average number of (x context) we can expect is (expected value).

Interpret binomial mean (μx)

After many, many trials, the average number of (success context) out of (n) is (μx).

Interpret binomial SD (ox)

The number of (success context) out of (n) typically varies by (ox) from the mean of (μx).

Transforming random variables (multiple/divide by A)

- Mean - multiply or divide by A - SD - multiply or divide by A - Variance - multiply or divide the SD by A^2

Transforming random variables (add/subtract A)

- Mean - add or subtract by A - SD - no change - Variance - no change

Combining random variables (S = X + Y)

- μ = μx + μy - o = √ox^2 + oy^2 - o = ox^2 + oy^2

Combining random variables (D = X - Y)

- μ = μx - μy - o = √ox^2 + oy^2 - o = ox^2 + oy^2

Calculate normal distribution probability (more/less than)

normalcdf(>, <, μ, o)

Calculate normal distribution (gives % on curve)

inversecdf(area, μ, o)

Identifying when to use geometric distributions

"On any given ___, there is a ___% probability..."

Describing a geometric distribution

Conditions: BIFS - Binary - success or failures - Independence - First success - Same probability - Shape - Center - μx = 1/p - Variability - ox = √(1-p)/p

Find the probability of a geometric distribution (until)

geometricpdf(p, x)

Find the probability of a geometric distribution (within)

geometriccdf(p, lower, upper)

Sampling distribution

Many, many samples and a statistic calculated for each of those samples

What makes a good statistic?

- No bias - Low variability

Z score for one sample proportion

z = (p (hat) - p) / √p(1-p)/n

Z score for one sample mean

z = (x̄ - μ) / o/√n

Calculate z score into p-value

normcdf(z score, 1E99, 0, 1)

Interpret standard deviation of sample proportions (op(hat))

The sample proportion of (success context) typically varies by (op(hat)) from the true proportion of (p).

Standard deviation of sample means (ox̄)

The sample mean amount of (x-context) typically varies by (ox̄) from the true mean of (μx).

One sample confidence interval for mean (μ)

1) State: μ = true mean (context) CL = ___ 2) Plan: name: one sample t interval for μ Conditions: 1) random 2) 10% rule 3) normal - pop. distribution is normal, CLT (n ≥ 30), graph shows no strong skew or outliers 3) Do: x +/- t* (S/√n) 4) Conclude: We are (CL)% confident that the interval from ___ to ___ captures the true mean of (context).

One sample confidence interval for proportions (p)

1) State: p = true proportion (context) CL = ___ 2) Plan: name: one sample z interval for p Conditions: 1) random 2) 10% rule 3) normal - CLT (n ≥ 30) 3) Do: p(hat) +/- z* (√(p(hat)(1-p(hat))/n 4) Conclude: We are (CL)% confident that the interval from ___ to ___ captures the true proportion of (context).