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| 6265459092 | Mean | Sum of observations/Number of Observations |  | 0 |
| 6265459093 | IQR | Q3-Q1 Resistant to outliers | 1 | |
| 6265459094 | Standard Deviation | Common measure of spread. How far each observation is from the mean. Found with an average of the squared distances. Then taking the squared root. Avg squared distance: VARIANCE Square root of Var: STANDARD DEV |  | 2 |
| 6265459095 | Measures of Position | Percentiles: Percentile tells us a data point's position relative to other points in the data set. 85% (then that student scored higher than 85% of the students taking the SAT). Z-scores: Tells us a data point's position relative to the mean and measured in "standard" units or in standard deviations. |  | 3 |
| 6265459096 | Density Curve | Math model for a distribution. Shows the overall pattern of a distribution via a smooth curve, ignoring minor irregularities and outliers. | 4 | |
| 6265459097 | Area under curve | Relative frequency of values in distribution. Always on or above horizontal axis. Total area underneath curve is exactly one. | 5 | |
| 6265459098 | Mean + Median for Density Curve | Median of a density curve: Equal-areas point, the point that divides the area under the curve in half. Mean of a density curve: Balance point, at which the curve would balance if made of solid material. Median + Mean: Same for symmetric density curve, both lie at center Mean of skewed curve: Pulled away from median in direction of tail. Median is not at peak, but not affected by skew. | 6 | |
| 6265459099 | Transforming Data | Mean: Changes when added to, also when multiplied Median: Changes when added to, also when multiplied Range/IQR: Does not change when addition, changes when multiplied St. Dev: Doesn't change when addition, changes when multiplied | 7 | |
| 6265459100 | Normal Distribution | All: Symmetric, single-peaked, bell-shaped Described with Mean, Standard deviation Low standard deviation = high peak Mean= center Standard deviation= center of inflection point Describes as: APPROXIMATELY NORMAL | 8 | |
| 6265459101 | Assessing Normality | #1 Histogram or stemplot: Test symmetry, bell-shaped #2 Empirical Rule (68%-95%-99.7%) Find the intervals, check the number and percent of data that appears within standard deviations from the sample mean. #3 Normal Probability Plot Found in Plot 1. Check if it is linear or not. | 9 | |
| 6265459102 | Expected Value of Discrete Random Variable (Mean) | Ux= E(X) = x1p1 + x2p2..... Multiply each probability with the value it represents. Add all. This gives equal representation of values. | 10 | |
| 6265459103 | Probability Distribution Standard Deviation | Var(x) = (X1-M1)^2p1 + ..... St Dev(X) = Root of Variance | 11 | |
| 6265459104 | Binomial Formula | P(X=k) = P(exactly K successes in trial) = (Failure) (Success) Binompdf(n, p, k) for P(X=k) Bimocdf(n, p, k) for P(X<=k) 1-Binomcdf(n, p, k) for P(X<=k) = P(x>=k) n= # of attempts p= probability of success 1-p=1 = probability of failure k= number of successes |  | 12 |
| 6265459105 | BINOMIAL DISTRIBUTION RULE | If the sample is less than 10% of the population, can ignore issue of replacement. n< N/10 n= sample size N= population size | 13 | |
| 6265459106 | Binomial Distribution SOCS | Shape: Depends of values of n, p Center: Mean=np Spread: Standard Dev= sqrt[ n * P * ( 1 - P ) ] | 14 | |
| 6265459107 | Rule of Thumb for using normal distribution for the approximation of the binomial distribution | If np> 10 and n(1-p)10>10 It means it is approximately normal | 15 | |
| 6265459108 | Geometric Formulas | P (x=k) = p (1-p) ^(k-1) P(x<=k) = p+ (1-p)p =(1-p)^2(p).... P(x>k)= 1-P(x<=k) Geompdf(p,k) = P(x=k) Geomcdf(p,k) = P(x<=k) | 16 | |
| 6265459110 | Manipulating Normal Distributions | Random variable y=x+c Mean(y): Mean(x) + c Variance(y): Variance(x) Deviation(y): Deviation(x) Random variable z= bx Mean(z)= Mean(x) X b Variance(z)= Variance(z) X b^2 Deviation(z)= Deviation(w) X (abs value of b) Random variable w=bx+c Mean(w)=Mean(w) X b +c Variance(w)= Variance(w) X b^2 Deviation(w)= Deviation(w) X (abs value of b) | 17 | |
| 6265459111 | Combining Probability Distributions | Mean(y-x)= Mean(y)-Mean(x) Standard Deviation(y-x)= Square root[ dev(x)^2 + dev(y)^2) ] Mean (x+y) = Mean(x)+Mean(y) Standard Deviation(x+y)= Square root[ dev(x)^2 + dev(y)^2) ] | 18 |
