AP Statistics Chapter 2

The pth percentile of a distribution is the value with p percent of values lower than it. Calculated by dividing the number of values less than p divided by the total number of values.
Frequency Graph
A graph showing the counts of each class in a distribution.
Relative Frequency Graph
A graph showing the percent values of each class from the whole.
Cumulative Relative Frequency Graph
The cumulative relative frequency of successive class is the relative frequency of that class added to the ones below it. Graphed by plotting a point corresponding to each class at the smallest value of the next class.
The conversion of observations from original values to standard deviation values. Used to compare observations from different distributions on a common scale.
Standardized Score
Also known as the z-score. Tells how many standard deviations from the mean an observation is, and in what direction.

Calculated using the following formula:

(X - Mean) / Standard Deviation
Transforming Data
Converts the observation from the original units of measurement to a standardized scale.
Adding/Subtracting a Constant
Affects measures of center, but not shape or spread, shifting them by adding/subtracting the constant to those measures.
Multiply/Dividing a Constant
Affects measures of center and spread, but not shape, multiplying/dividing these measures by the constant.
Density Curve
A density curve describes the overall pattern of a distribution. The area under this curve and above any intervals on the axis is the proportion of all observations falling into that interval.

Density curves always:
1. Are on or above the horizontal axis
2. Have an area of 1 under the curve.
Median of Density Curve
The equal-areas point of a density curve, at which area is equal on either side.
Mean of Density Curve
The balancing point of a density curve, where the curve would balance if made of solid material.
Normal Distribution
A distribution that is described by a normal density curve, and is completely specified by its mean, μ (mu), and its standard deviation σ (sigma). Abbreviated by N(μ, σ).
Normal Curve
A symmetric, single-peaked, and bell-shaped curve, that describes a normal distribution. The mean μ is located at the center of the curve, and the standard deviation σ is the distance from the center to the inflection points on either side.
68-95-99.7 Rule
Formally known as the Empirical Rule, this states that nearly all data in a normal distribution falls within 3 standard deviations of the mean, and that 68% of the observations are in the first standard deviation, 95% in the first two, and 99.7 in the first three.
Standard Normal Distribution
A normal distribution with a mean of 0 and a standard deviation of 1.
Standard Normal Table
Also known as Table A, this is a table of the areas underneath a standard normal curve. It gives the area to the left of a specific z-value.

The left side of the table represents the first two digits (ones digit and tenths digit) of your z-value, and the top side represents the final digit (hundredths digit), and the value corresponding to that row and column in the table is the desired area.
Command used on a TI-83/84 calculator (command is normalCdf( on TI-89) to find the area to the left of a specific z-value on a normal curve, given the following values:

normalcdf(lower bound, upper bound, mean, standard deviation)
Command used on a TI-83/84/89 calculator to find the value corresponding to a given area to the left of that value, given the following values:

invNorm(area to the left, mean, standard deviation)
Normal Probability Plot
Used to assess if a data set follows a normal distribution.

Steps for Creating
1. Order each observation smallest to largest, recording the percentile for each observation.
2. Using Table A or invNorm(, find the z-scores for each percentile.
3. Plot each observation x against its expected z-score.

If the line created is roughly linear, the distribution is normal. Only pay attention to systematic deviations from the line, not few far away points, which are outliers.
Pat did better than 73% of the test takers
Suppose 1000 students take a standardized test. Pat earned a score of 63, which placed him at the 73rd percentile. This means...