Chapter 2 notes are completed! Again, the info in the links are not created by me and are just extra info I found helpful. Chapter 3 notes should be up soon. Hope this is helpful!

Ch 2: Describing Location in a Distribution

Part 1: Measures of Relative Standing and Density Curves

• Shows relatives standings with numbers
• if distribution is roughly symmetric with no obvious outliers... mean is around the same as the average
• we can calculate with z-scores
• x-score = (x-mean)/(standard deviation)
• called standardizing, so the z-score is also called the standardized value
• tells how many standard deviations away from mean a value is
• can be used to compare numbers
• z-scores to percentiles
• can use Chebyshev’s inequality
• can be used in any distribution
• percent of observations falling within k standard deviations from the mean is at least (100)(1-1/k2)
• for example, if k = 1, at least 0% of observations will fall within 1 standard deviation of the mean
• shows that it is unusual to find observation more than 5 standard deviations from the mean
• gives us insight into how observations are distributed, but not percentiles; need density curves to do that
• density curves: always on or above horizontal axis and has area of 1
• the curve better to use than histograms because does not depend on our choices
• describes overall pattern of distribution; doesn’t accurately describe data, but accurately enough for use
• come in many shapes; one kind is a normal shape
• Mean and median in density curves
• median: equal-areas point, and if the curve is Normal, then median is its center
• mean:  balancing point of any(?) distribution, including density curves
• in a symmetric curve, these two are equal; in a Normal curve, then these two are approximately equal (?)
• notations
• X-bar and s for mean and stan. dev. in actual observations (data), M and O-- for density curves

Part 2: Normal Distributions

• Normal distributions: symmetrical, bell-shaped density curves; they are special curves
• all have similar shape, and are described by M (mean) and O-- (standard deviation)
• N(Mean, Stan. dev.)
• 68-95-99.7 rule: around 68% observations fall within 1 stan. dev. from mean, around 95% observations fall within 2 stan. dev. from mean, and around 99.7% observations fall within 3 stan. dev. from mean
• more precise than Chebyshev’s rule
• standard Normal distribution: distribution of the z-score, if the original variable also have a normal distribution
• standardizing is also a linear transformation
• can calculate percentiles using Table A, or the standard Normal table
• calculate z-score to two decimal places, then use the table to find the percentage to the left of the z-score (less than the z-score or the indicated value)
• if want to calculate percentage more than the value, then use 1 - indicated percentage
• to answer question, answer in context and is reasonable
• ex: If Sasha got a score of x in the test that has the normal distribution of N(M, O--), what is her percentile? Answer: Sasha’s percentile will be ___ if she got a score of x.
• always sketch the curve, mark z-score, then shade area of interest
• Summary of calculating
• find what the question is asking and what variable it is stating and draw and shade distribution; calculate z-score and mark that
• use the table and find corresponding percents
• answer question in context
• if the z-scores exceed the values given by Table A, then take the Table’s percentages as 0 (if the scores are negative) or 100 (if the scores are positive)
• Finding value given the proportion
• the process is basically just the backwards of finding the proportion
• find corresponding proportion, then find the z-score, then use the z-score equation to solve for x
• Determining if the data is Normal
• make histogram or stemplot and see if graph is around bell-shaped and symmetric around mean
• use normality plot; if lie in straight line, then data is Normal; if a point is far away from overall pattern, then it is an outlier
• to do this, plot the z-scores on the x-axis, and data on the y-axis...
• turn on a plot, and select the lower-last picture of a plot; that is the normality plot
• if the plot is not linear...
• if the largest observations are distinctly above the line drawn through the main body of plots, then it is skewed right
• if smallest observations distinctly below the line drawn through main body of plots, then it is skewed left
• only concentrate on shapes that are distinctly not linear, and ignore the wiggles

more vocab and concepts

http://quizlet.com/18419988/ap-statistics-chapt-2-flash-cards/