AP Statistics Formula Cheat Sheet and Tables, Cheat Sheet of Statistics

Download AP Statistics Formula Cheat Sheet and Tables and more Cheat Sheet Statistics in PDF only on Docsity! Formulas and Tables for AP Statistics I. Descriptive Statistics 1 i i xx xn n ∑ = ∑ = ( ) ( ) 2 21 1 1 i x i x xs x xn n ∑ − = ∑ − = − − ŷ a bx= + y a bx= + 1 1 i i x y x x y yr n s s − −  = ∑  −    y x b r s= s II. Probability and Distributions ( ) ( ) ( ) ( )P A B P A P B P A B∪ = + − ∩ ( ) ( )( )| P A BP A B P B ∩ = Probability Distribution Mean Standard Deviation Discrete random variable, X µ =X E (X ) = ∑ x Pi (x )i σ X = ∑ −xi X P xi µ( ) 2 ( ) If 𝑋𝑋 has a binomial distribution with parameters n and p, then: nP X( = x) =  px (1 − p) n x−   x  where x = 0, 1, 2, 3, ,n µ =X np σ =X np (1 − p) If 𝑋𝑋 has a geometric distribution with parameter p, then: P X( = x) = (1 − p)x−1 p where x = 1, 2, 3, 1µ =X p 1 − pσ =X p III. Sampling Distributions and Inferential Statistics Standardized test statistic: statistic parameterstandard error of the statistic − Confidence interval: ( )( )statistic critical value standard error of statistic± Chi-square statistic: ( )2 observed expectedexpectedχ − = ∑ 2 AP Statistics 2020 Formulas and Tables Sheet *S tandard deviation is a measurement of variability from the theoretical population. Standard error is the estimate of the standard deviation. If the standard deviation of the statistic is assumed to be known, then the standard deviation should be used instead of the standard error. III. Sampling Distributions and Inferential Statistics (continued) Sampling distributions for proportions: Random Variable Parameters of Sampling Distribution Standard Error* of Sample Statistic For one population: p̂ −(1 )pσ p̂ = n µ p̂ = p p p̂ (1 − )s p̂ = n p̂ For two populations: p −1 pˆ ˆ2 µ = p −p pˆ ˆ− 11 2 p p (1 −σ 1 p p1 2) ( )= +p pˆ ˆ−1 2 n1 − p1 22 n2 p̂ s 1 1 − p pˆ ˆ1 2= +p pˆ ˆ−1 2 n1 ( 1 −) ( p̂2 ) n2 When p =1 is assumed: p2 s = p p( 1ˆ ˆ1 −p pˆ ˆ− c c )1 2  n n1 1 +  2  X X+ p̂ = 1c n n+where 2 1 2 Sampling distributions for means: Random Variable Parameters of Sampling Distribution Standard Error* of Sample Statistic For one population: X µ = X σσ =X n µ ss =X n For two populations: X X−1 2 µ = µ −X X− 1 1 2 µ2 σ σ2 2 σ = 1 2+X X−1 2 n1 2n s s2 s = 1 +X X−1 2 n n1 2 2 2 Sampling distributions for simple linear regression: Random Variable Parameters of Sampling Distribution Standard Error* of Sample Statistic For slope: b σσ =b , σ x n ( )2∑ −x x σ = ix nwhere ss =b ,s n − 1x ( ˆ )2∑ −y y s = i i − n 2 ( )2∑ −x x s = ix n − 1and where AP Statistics 2020 Formulas and Tables Sheet b =µ β Table B t distribution critical values Tail probability p df .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .001 .0005 1 1.000 1.376 1.963 3.078 6.314 12.71 15.89 31.82 63.66 127.3 318.3 636.6 2 .816 1.061 1.386 1.886 2.920 4.303 4.849 6.965 9.925 14.09 22.33 31.60 3 .765 .978 1.250 1.638 2.353 3.182 3.482 4.541 5.841 7.453 10.21 12.92 4 .741 .941 1.190 1.533 2.132 2.776 2.999 3.747 4.604 5.598 7.173 8.610 5 .727 .920 1.156 1.476 2.015 2.571 2.757 3.365 4.032 4.773 5.893 6.869 6 .718 .906 1.134 1.440 1.943 2.447 2.612 3.143 3.707 4.317 5.208 5.959 7 .711 .896 1.119 1.415 1.895 2.365 2.517 2.998 3.499 4.029 4.785 5.408 8 .706 .889 1.108 1.397 1.860 2.306 2.449 2.896 3.355 3.833 4.501 5.041 9 .703 .883 1.100 1.383 1.833 2.262 2.398 2.821 3.250 3.690 4.297 4.781 10 .700 .879 1.093 1.372 1.812 2.228 2.359 2.764 3.169 3.581 4.144 4.587 11 .697 .876 1.088 1.363 1.796 2.201 2.328 2.718 3.106 3.497 4.025 4.437 12 .695 .873 1.083 1.356 1.782 2.179 2.303 2.681 3.055 3.428 3.930 4.318 13 .694 .870 1.079 1.350 1.771 2.160 2.282 2.650 3.012 3.372 3.852 4.221 14 .692 .868 1.076 1.345 1.761 2.145 2.264 2.624 2.977 3.326 3.787 4.140 15 .691 .866 1.074 1.341 1.753 2.131 2.249 2.602 2.947 3.286 3.733 4.073 16 .690 .865 1.071 1.337 1.746 2.120 2.235 2.583 2.921 3.252 3.686 4.015 17 .689 .863 1.069 1.333 1.740 2.110 2.224 2.567 2.898 3.222 3.646 3.965 18 .688 .862 1.067 1.330 1.734 2.101 2.214 2.552 2.878 3.197 3.611 3.922 19 .688 .861 1.066 1.328 1.729 2.093 2.205 2.539 2.861 3.174 3.579 3.883 20 .687 .860 1.064 1.325 1.725 2.086 2.197 2.528 2.845 3.153 3.552 3.850 21 .686 .859 1.063 1.323 1.721 2.080 2.189 2.518 2.831 3.135 3.527 3.819 22 .686 .858 1.061 1.321 1.717 2.074 2.183 2.508 2.819 3.119 3.505 3.792 23 .685 .858 1.060 1.319 1.714 2.069 2.177 2.500 2.807 3.104 3.485 3.768 24 .685 .857 1.059 1.318 1.711 2.064 2.172 2.492 2.797 3.091 3.467 3.745 25 .684 .856 1.058 1.316 1.708 2.060 2.167 2.485 2.787 3.078 3.450 3.725 26 .684 .856 1.058 1.315 1.706 2.056 2.162 2.479 2.779 3.067 3.435 3.707 27 .684 .855 1.057 1.314 1.703 2.052 2.158 2.473 2.771 3.057 3.421 3.690 28 .683 .855 1.056 1.313 1.701 2.048 2.154 2.467 2.763 3.047 3.408 3.674 29 .683 .854 1.055 1.311 1.699 2.045 2.150 2.462 2.756 3.038 3.396 3.659 30 .683 .854 1.055 1.310 1.697 2.042 2.147 2.457 2.750 3.030 3.385 3.646 40 .681 .851 1.050 1.303 1.684 2.021 2.123 2.423 2.704 2.971 3.307 3.551 50 .679 .849 1.047 1.299 1.676 2.009 2.109 2.403 2.678 2.937 3.261 3.496 60 .679 .848 1.045 1.296 1.671 2.000 2.099 2.390 2.660 2.915 3.232 3.460 80 .678 .846 1.043 1.292 1.664 1.990 2.088 2.374 2.639 2.887 3.195 3.416 100 .677 .845 1.042 1.290 1.660 1.984 2.081 2.364 2.626 2.871 3.174 3.390 1000 .675 .842 1.037 1.282 1.646 1.962 2.056 2.330 2.581 2.813 3.098 3.300 • .674 .841 1.036 1.282 1.645 1.960 2.054 2.326 2.576 2.807 3.091 3.291 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% Confidence level C Probability p t* Table entry for p and C is the point t* with probability p lying above it and probability C lying between t* and t*. AP Statistics 2020 Formulas and Tables Sheet Table C c2 critical values Tail probability p df .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .001 .0005 1 1.32 1.64 2.07 2.71 3.84 5.02 5.41 6.63 7.88 9.14 10.83 12.12 2 2.77 3.22 3.79 4.61 5.99 7.38 7.82 9.21 10.60 11.98 13.82 15.20 3 4.11 4.64 5.32 6.25 7.81 9.35 9.84 11.34 12.84 14.32 16.27 17.73 4 5.39 5.99 6.74 7.78 9.49 11.14 11.67 13.28 14.86 16.42 18.47 20.00 5 6.63 7.29 8.12 9.24 11.07 12.83 13.39 15.09 16.75 18.39 20.51 22.11 6 7.84 8.56 9.45 10.64 12.59 14.45 15.03 16.81 18.55 20.25 22.46 24.10 7 9.04 9.80 10.75 12.02 14.07 16.01 16.62 18.48 20.28 22.04 24.32 26.02 8 10.22 11.03 12.03 13.36 15.51 17.53 18.17 20.09 21.95 23.77 26.12 27.87 9 11.39 12.24 13.29 14.68 16.92 19.02 19.68 21.67 23.59 25.46 27.88 29.67 10 12.55 13.44 14.53 15.99 18.31 20.48 21.16 23.21 25.19 27.11 29.59 31.42 11 13.70 14.63 15.77 17.28 19.68 21.92 22.62 24.72 26.76 28.73 31.26 33.14 12 14.85 15.81 16.99 18.55 21.03 23.34 24.05 26.22 28.30 30.32 32.91 34.82 13 15.98 16.98 18.20 19.81 22.36 24.74 25.47 27.69 29.82 31.88 34.53 36.48 14 17.12 18.15 19.41 21.06 23.68 26.12 26.87 29.14 31.32 33.43 36.12 38.11 15 18.25 19.31 20.60 22.31 25.00 27.49 28.26 30.58 32.80 34.95 37.70 39.72 16 19.37 20.47 21.79 23.54 26.30 28.85 29.63 32.00 34.27 36.46 39.25 41.31 17 20.49 21.61 22.98 24.77 27.59 30.19 31.00 33.41 35.72 37.95 40.79 42.88 18 21.60 22.76 24.16 25.99 28.87 31.53 32.35 34.81 37.16 39.42 42.31 44.43 19 22.72 23.90 25.33 27.20 30.14 32.85 33.69 36.19 38.58 40.88 43.82 45.97 20 23.83 25.04 26.50 28.41 31.41 34.17 35.02 37.57 40.00 42.34 45.31 47.50 21 24.93 26.17 27.66 29.62 32.67 35.48 36.34 38.93 41.40 43.78 46.80 49.01 22 26.04 27.30 28.82 30.81 33.92 36.78 37.66 40.29 42.80 45.20 48.27 50.51 23 27.14 28.43 29.98 32.01 35.17 38.08 38.97 41.64 44.18 46.62 49.73 52.00 24 28.24 29.55 31.13 33.20 36.42 39.36 40.27 42.98 45.56 48.03 51.18 53.48 25 29.34 30.68 32.28 34.38 37.65 40.65 41.57 44.31 46.93 49.44 52.62 54.95 26 30.43 31.79 33.43 35.56 38.89 41.92 42.86 45.64 48.29 50.83 54.05 56.41 27 31.53 32.91 34.57 36.74 40.11 43.19 44.14 46.96 49.64 52.22 55.48 57.86 28 32.62 34.03 35.71 37.92 41.34 44.46 45.42 48.28 50.99 53.59 56.89 59.30 29 33.71 35.14 36.85 39.09 42.56 45.72 46.69 49.59 52.34 54.97 58.30 60.73 30 34.80 36.25 37.99 40.26 43.77 46.98 47.96 50.89 53.67 56.33 59.70 62.16 40 45.62 47.27 49.24 51.81 55.76 59.34 60.44 63.69 66.77 69.70 73.40 76.09 50 56.33 58.16 60.35 63.17 67.50 71.42 72.61 76.15 79.49 82.66 86.66 89.56 60 66.98 68.97 71.34 74.40 79.08 83.30 84.58 88.38 91.95 95.34 99.61 102.7 80 88.13 90.41 93.11 96.58 101.9 106.6 108.1 112.3 116.3 120.1 124.8 128.3 100 109.1 111.7 114.7 118.5 124.3 129.6 131.1 135.8 140.2 144.3 149.4 153.2 Probability p (χ2) Table entry for p is the point ( 2 ) with probability p lying above it. AP Statistics 2020 Formulas and Tables Sheet