Modeling Distributions of Data
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| 8006070824 | Percentile | 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. | 0 | |
| 8006070825 | Frequency Graph | A graph showing the counts of each class in a distribution. | 1 | |
| 8006070826 | Relative Frequency Graph | A graph showing the percent values of each class from the whole. | 2 | |
| 8006070827 | 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. | 3 | |
| 8006070828 | Standardizing | The conversion of observations from original values to standard deviation values. Used to compare observations from different distributions on a common scale. | 4 | |
| 8006070829 | 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 | 5 | |
| 8006070830 | Transforming Data | Converts the observation from the original units of measurement to a standardized scale. | 6 | |
| 8006070831 | Adding/Subtracting a Constant | Affects measures of center, but not shape or spread, shifting them by adding/subtracting the constant to those measures. | 7 | |
| 8006070832 | Multiply/Dividing a Constant | Affects measures of center and spread, but not shape, multiplying/dividing these measures by the constant. | 8 | |
| 8006070833 | 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. | 9 | |
| 8006070834 | Median of Density Curve | The equal-areas point of a density curve, at which area is equal on either side. | 10 | |
| 8006070835 | Mean of Density Curve | The balancing point of a density curve, where the curve would balance if made of solid material. | 11 | |
| 8006070836 | 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). | 12 | |
| 8006070837 | 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. | 13 | |
| 8006070838 | 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. | 14 | |
| 8006070839 | Standard Normal Distribution | A normal distribution with a mean of 0 and a standard deviation of 1. | 15 | |
| 8006070840 | 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. |  | 16 |
| 8006070841 | normalcdf( | 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) | 17 | |
| 8006070842 | invNorm( | 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) | 18 | |
| 8006070843 | 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. | 19 | |
| 8006070844 | 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... | 20 |
