PSDA CRAM

What is the formula for percent change?

(new - original / original ) x 100%

What is the difference between a percentage-point increase and a percent increase?

Percentage points = subtraction.
Percent increase = divide the change by the original.

How do you increase a number by r%?

multiply by 1 + (r/100)

How do you decrease a number by r%?

multiply by 1- (r/100)

A quantity increases 20% and then decreases 20%. Does it return to its original value?

No.

1.20(0.80)=0.96

It's a 4% decrease overall.

If A is 25% greater than B, what equation represents this?

A=1.25B

Q: If A is 25% less than B, what equation represents this?

A=0.75B

Q: If A is 25% of B, what equation represents this?

A=0.25B

If a final value is known after a 20% increase, how do you find the original?

divide by 1.20

mean formula

mean = sum/number of values

if the mean of n numbers is m, what is their total sum?

sum = nm

what is the weighted average?

(value)(weight) + (value)(weight) / weights

Can you average two averages by simply adding them and dividing by 2?

Only if the two groups have equal sizes.

Otherwise use a weighted average.

what happens to the mean if you add k to every value?

the mean increases by k

what happens to the median if you add k to every value

the median increases by k

what happens to the range if you add k to every value?

nothing

what happens to standard deviation if you add the same number to every value?

it stays the same

what happens to standard deviation if every value is multiplied by 3?

stdev is multiplied by 3

what does a larger stdev mean?

data more spread out

what does a smaller stdev mean?

data more tightly clustered

what is basic probability?

p(E) = favorable outcomes/total outcomes

what is the complement rule?

p(Not A) = 1 - P(A)

what is the probability of A AND B for independent events?

p (A AND B) = P(A)P(B)

what is the probability of A OR B

P (A or B) = P(A) + P(B) - P (A AND B)

when can you simply add P(A) + P(B)

when A and B are mutually exclusive, they cannot happen simultaneously

what is conditional probability?

what does the phrase “given that” usually signal?

conditional probability

how do you solve “at least one” probability questions?

P(at least one) = 1- P(none)

if the probability of success is p, what is the probability of failure?

1-P

in a conditional probability question, what determines the denominator?

A: The condition.

If asked:

Probability of A given B

your denominator is everyone in B.

If 12 of 40 students who play sports are girls, what is P(girl∣sports)

12/40, The denominator is the sports group because you're given that the student plays sports.

What is the fastest way to avoid two-way-table mistakes?

Circle the condition and use its total as the denominator.

What is the difference between a population and a sample?

Population: entire group being studied.
Sample: subset of the population.

: What does random sampling allow you to generalize to?

A: The population.

What does random assignment allow you to determine?

Whether there is evidence that a treatment causes an outcome.

What's the difference between random sampling and random assignment?

random sampling is for generalization, random assignment is for causation

can an observational study establish causation?

generally no, makes association

what does correlation mean?

2 variables r associated in some way

what does correlation not equal to causation mean?

An association between two variables doesn't prove that changing one variable causes a change in the other.

What is voluntary response bias?

A: People choose whether to participate, often causing people with stronger opinions to be overrepresented.

Q: What is nonresponse bias?

A: People selected for the sample don't respond, and their absence may make the sample unrepresentative.

What is undercoverage?

Some members/groups of the population have little or no chance of being selected

What is a convenience sample?

A sample chosen because participants are easy to reach.

Q: What does a positive association mean?

as x increases y tends to increase

what does a negative association mean?

as x increase y decrease

what indicates a strong linear association?

points are tightly clustered around a line

r about equal to 1 means…

means a strong positive linear association

what does r about equal to -1 mean

means a strong negative linear association

what does r about equal to 0 mean?

little/no linear association

what is the equation of a linear model

y=mx+b

What does the slope mean in a data context?

The predicted change in y for every 1-unit increase in x.

residual formula

residual = actual - predicted

what does a positive residual mean?

actual value is above the predicted value

what does a negative residual mean?

actual value is below the predicted value

what does r squared represent?

the approximate proportion of variation in y explained by the linear model

if r = 0.8, what is r squared?

0.64, so 64% of the variation is explained

what is the general exponential model>

y=a(b)^x​

in y=a(b)^x​, what does a represent

the initial value when x = 0

in exponential form what does b > 1 indicate?

exponential growth

in exponential form what does 0 < b < 1 indicate?

exponential decay

how do u represent 8% exponential growth?

1.08 is exponential growth

how do u represent exponential decay?

0.92 is exponential decay

if a population grows 5% per year, and the initial population is 2000

2000(1.05) raised to t, which represents years

what is the basic rate formula?

rate = quantity/time

what is the distance formula?

d=rt

what is the most important rule for unit conversions?

make unwanted units cancel

can you average 2 speeds by simply doing r1+r2/2?

not neccesarily, avg speed is total distance/total time

a value goes from 40 to 50 whats the percent increase?

25% not 20

A value is 25% greater than another value. Is the smaller value 25% less than the larger value?

A: No.

If B=1.25A, then:

B−A​/B=0.25A/1.25A​=20%

So the smaller value is 20% less.

which denominator do you uses for percent change

the original value

if every value in a data set is increased by 10 what happens

up 10, nothing happens

if every value is multiplied by 10, what happens to standard deviation?

it becomes 10 times larger

“at least one” what should u think?

us the complement

“given that” what should u think?

conditional probability

What's the fastest PSDA strategy when a question gives you a huge table?

A: Don't calculate everything. Identify exactly what the question asks for, locate only the relevant rows/columns, then calculate.

PRIORITY

1. Percent change = (new−old)/old

2. Increase r% → × 1+r

3. Decrease r% → × 1−r

4. Mean = sum / number

5. Sum = mean × number

6. Weighted average = weighted sum / total weight

7. P(not A)=1−P(A)

8. "At least one" → 1−P(none)

9. "Given that" → conditional probability

10. Random sample → generalization

11. Random assignment → causation

12. Correlation ≠ causation

13. Residual = actual − predicted

14. Exponential growth → a(1+r)x

15. Average rate = total quantity / total time