Quarter 4 Class Notes
Unit 11- Statistics
5/24- Margin of Error
*MOE occurs about 2 standard deviations from the mean. It accounts for our 95% confidence interval.
*To determine a range for the population proportion, add and subtract the MOE to the sample proportion.
*MOE occurs about 2 standard deviations from the mean. It accounts for our 95% confidence interval.
*To determine a range for the population proportion, add and subtract the MOE to the sample proportion.
5/23- Population & Sample Proportions, Confidence Intervals
*Sample proportion = # who "did something" out of the total sample.
*Population proportion = # who "did something" out of total population.
*Confidence Interval- about 2 standard deviations away from the mean proportion. Data that falls within about 95% of out simulation data distributions. Be careful to read each question and answer accordingly!
*Sample proportion = # who "did something" out of the total sample.
*Population proportion = # who "did something" out of total population.
*Confidence Interval- about 2 standard deviations away from the mean proportion. Data that falls within about 95% of out simulation data distributions. Be careful to read each question and answer accordingly!
5/12, 5/21- Normal Distributions
*If data is normalized, then you may use a normal curve to represent the data.
*The mean = median = mode on a normal curve.
*Standard deviation tells you how "normal" your score was compared to the average (mean).
*You can determine percentages based on the normal curve by adding within intervals.
*normalcdf is used on calculator to determine probabilities or percentages between 2 scores. Go to 2nd VARS and then hit choice 2.
*invnorm is used when we know the area (prob./ percentage) under the curve and are looking for a specific data point that falls at this percentage. Get to this key by hitting 2nd VARS, then choice 3.
*If data is normalized, then you may use a normal curve to represent the data.
*The mean = median = mode on a normal curve.
*Standard deviation tells you how "normal" your score was compared to the average (mean).
*You can determine percentages based on the normal curve by adding within intervals.
*normalcdf is used on calculator to determine probabilities or percentages between 2 scores. Go to 2nd VARS and then hit choice 2.
*invnorm is used when we know the area (prob./ percentage) under the curve and are looking for a specific data point that falls at this percentage. Get to this key by hitting 2nd VARS, then choice 3.
5/11- Mean, Standard Deviation, and Variance
*Mean = x bar
*SD = population standard deviation (lower case sigma)
*Variance: Go to your home screen, hit 2nd STAT, arrow over to MATH, then hit 8. Be sure to type in a LIST
*Be sure to show all work and then round your answers!
*Mean = x bar
*SD = population standard deviation (lower case sigma)
*Variance: Go to your home screen, hit 2nd STAT, arrow over to MATH, then hit 8. Be sure to type in a LIST
*Be sure to show all work and then round your answers!
5/10- Intro to Stats
*Make sure to understand basic statistical vocabulary (bias, population, sample, etc.)
*Make sure you know the difference between a survey, a controlled experiment, and an observational study.
*Make sure to understand basic statistical vocabulary (bias, population, sample, etc.)
*Make sure you know the difference between a survey, a controlled experiment, and an observational study.
Unit 10- Probability
5/3- Proving Independence for Events
*To prove 2 events are independent, you can prove P(A given B) = P(A) OR prove that P(A and B) = P(A) times P(B)
*To prove 2 events are independent, you can prove P(A given B) = P(A) OR prove that P(A and B) = P(A) times P(B)
4/30- Independent vs. Dependent Events
*Independent Events- event that does not affect the outcome of another event. (Example- roll a die and then flip a coin)
*Dependent Events- event that does affect the outcome of another event (Example- pick a ball out of a bag and don't replace it. Then pick another ball)
*Events are independent of each other if P(A and B) = P(A) times P(B) or if the P(A) = P(A given that B has occurred).
*OR means to ADD, AND means to MULTIPLY!
*Independent Events- event that does not affect the outcome of another event. (Example- roll a die and then flip a coin)
*Dependent Events- event that does affect the outcome of another event (Example- pick a ball out of a bag and don't replace it. Then pick another ball)
*Events are independent of each other if P(A and B) = P(A) times P(B) or if the P(A) = P(A given that B has occurred).
*OR means to ADD, AND means to MULTIPLY!
4/28- Conditional Probability
*Probability of an event occurring, given that another event has already occurred.
*P(BOTH)/ P(GIVEN)
*Probability of an event occurring, given that another event has already occurred.
*P(BOTH)/ P(GIVEN)
4/26 & 27- Mutually Exclusive vs. Non Mutually Exclusive Events
*Mutually Exclusive Events: P(A or B) = P(A) + P(B)
*Non Mutually Exclusive Events: P(A or B) = P(A) + P(B) - "Overlap" (P(A AND B))
*Mutually Exclusive Events: P(A or B) = P(A) + P(B)
*Non Mutually Exclusive Events: P(A or B) = P(A) + P(B) - "Overlap" (P(A AND B))
4/25- Basic Probability
*Probability = N(possible times the event occurs)/ N(total number of events)
*Probability = N(possible times the event occurs)/ N(total number of events)
UNIT 9- Sequences, Series, Regressions
4/18 & 4/19- Regressions & Average Rate of Change
*Make sure you have STAT DIAGNOSTICS ON in the mode of your calculator.
*Find any regression asked of you by going to STAT and entering 2 lists. Then go back to STAT and CALC the type of regression you want.
*Be careful rounding!
*Average Rate of Change- the slope of the secant line to a non-linear function. (Change of y over the change of x)
*Make sure you have STAT DIAGNOSTICS ON in the mode of your calculator.
*Find any regression asked of you by going to STAT and entering 2 lists. Then go back to STAT and CALC the type of regression you want.
*Be careful rounding!
*Average Rate of Change- the slope of the secant line to a non-linear function. (Change of y over the change of x)
4/16- Geometric Series
*The sum of a geometric sequence is called a geometric series.
*The formula for this is on your reference sheet.
*Be careful to answer the question!!!
*Sigma is a Greek letter that adds the terms of a sequence.
*To get to sigma, hit ALPHA WINDOW 2.
*Be sure to use an extra set of parenthesis!!!
*The sum of a geometric sequence is called a geometric series.
*The formula for this is on your reference sheet.
*Be careful to answer the question!!!
*Sigma is a Greek letter that adds the terms of a sequence.
*To get to sigma, hit ALPHA WINDOW 2.
*Be sure to use an extra set of parenthesis!!!
4/11- Converting Between Explicit & Recursive Formulas
*Determine if the sequence is arithmetic or geometric (is there a common difference or a common ratio).
*Use the reference sheet for explicit formulas.
*To write a recursive arithmetic sequence, it's the first term (an-1) + d. Always state the first term!
*To write a recursive geometric sequence, it's the first term (an-1) *r. Always state the first term!
*Determine if the sequence is arithmetic or geometric (is there a common difference or a common ratio).
*Use the reference sheet for explicit formulas.
*To write a recursive arithmetic sequence, it's the first term (an-1) + d. Always state the first term!
*To write a recursive geometric sequence, it's the first term (an-1) *r. Always state the first term!
4/10- Arithmetic & Geometric Sequences
*Arithmetic Sequences- move from term to term by adding (or subtracting).
*The common difference, d, is the amount you add to get to the next term.
*The formula to find any term of an arithmetic sequence is on your reference sheet!
*Geometric Sequences- move from term to term by multiplying (or dividing).
*The common ration, r, is the amount you multiply by to get to the next term.
*The formula to find any term of a geometric sequence is on your reference sheet.
*Arithmetic Sequences- move from term to term by adding (or subtracting).
*The common difference, d, is the amount you add to get to the next term.
*The formula to find any term of an arithmetic sequence is on your reference sheet!
*Geometric Sequences- move from term to term by multiplying (or dividing).
*The common ration, r, is the amount you multiply by to get to the next term.
*The formula to find any term of a geometric sequence is on your reference sheet.
4/9- Recursive Sequences
*A recursive sequence finds a term by using & knowing the previous term in a formula.
*A recursive sequence formula always has a starting value and is defined by the previous term.
*Be careful when you are substituting and evaluating.
*A recursive sequence finds a term by using & knowing the previous term in a formula.
*A recursive sequence formula always has a starting value and is defined by the previous term.
*Be careful when you are substituting and evaluating.
4/6- Venn Diagrams
*A AND B- events that occur in BOTH sets!
*A OR B- events that occur in either set (don't count the overlap twice!)
*A AND B- events that occur in BOTH sets!
*A OR B- events that occur in either set (don't count the overlap twice!)