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Stat Unit 2
| Term | Definition |
|---|---|
| when calculating z-score of a percentile > | subtract the percentage decimal from 100, put in invNorm, calculator always uses what is to the left of mean |
| percentile | the pth percentile is the value where p% of the data is less than or equal to it, us the word AT, can't be decimals, measure of position |
| when calculating z-score of a percentile < | is the percentage decimal, put in invNorm, use for percentiles |
| cumulative relative frequency graph | uses percentiles, Q1 = 25th percentile, median = 50th percentile, Q3 = 75th percentile |
| z-score of first quartile in a normal distribution | -0.67 |
| z-score of mean in a normal distribution | 0 |
| z-score of third quartile in a normal distribution | 0.67 |
| interpreting percentiles from a cumulative rel. frequency graph | (percentage/percentile) of (context) have (value from x-axis) or less |
| how to find a z-score | value - mean / standard deviation, involves 2 transformations (dividing and subtracting) |
| interpreting z-score | (context) is (z-score) standard deviations above/ below the mean, negative z-score = below mean, positive z-score = above mean |
| properties of graph after adding c | shape = same, center + c, spread = same |
| properties of graph after subtracting c | shape = same, center - c, spread = same |
| properties of graph after multiplying by c | shape = same, center x c, spread x c |
| properties of graph after dividing by c | shape = same, center / c, spread / c |
| mean and standard deviation when converting to z-scores | mean = 0, SD = 1 |
| uniform distribution | outcomes are equally likely, mean = median, symmetric |
| mu and lowercase sigma represent the | population |
| need to include on every normal distribution | N (mean, standard deviation) |
| empirical rule | 68% of data lies within 1 SD, 95% of data lies within 2 SDs, 99-100% of data lies within 3 SDs |
| SD outlier rule | if a data point is greater than 2 SDs away from the mean, it is an outlier |
| density curves | area = 1, x-axis is an asymptote |
| order of percentages in half of a normal curve | 0.15%, 2.35%, 13.5%, 34%, 34%, 13.5%, 2.35%, 0.15% |
| find % / area | use NormCdf and write low, high, mean, and SD |
| find boundary | find z-score of given %ile using the table, plug into z-score equation and solve for x, use invNorm and %ile to the left |
| checking for normality | 1. graph (does the dot plot/histogram look approx. normal?) 2. compare mean and median (are they almost the same/very close?) 3. Empirical Rule 4. normal probability plot (does the plot seem to be fairly linear?), if 1 test fails, it is NOT normal |
| checking for normality with the Empirical rule | put data values in table, use menu 611 to get the SD, find the endpoints of 1 SD above and below mean, find how many data points are in between these parameters, divide this # by the # of data values, see if it is close to 68% |
| finding cumulative relative frequency | add all of the previous relative frequencies to the relative frequency for the current row |
| how to find variance | square the standard deviation, do transformations first before squaring |
| is it normal? given max, mean, and SD | find the z-score of max value to justify why not (it is too close/too far from the mean to be normal) |
Created by:
ts2819