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AP STATS Unit 2
AP Statistics
| Term | Definition |
|---|---|
| Percentile | The percent of data values less than or equal to a given value |
| Standardized score | Data that we can use to compare data with very different values/units. Calculated as: z-score=(x-mean)/SD |
| Percentiles and z-scores | Can be both used to calculate for distributions with any shape |
| Add/Subtract "a" | Shape: same Center: +/- "a" Spread: same |
| Multi/Divide "b" | Shape: same Center: x/÷ "b" Spread: x/÷ "b" |
| Z-score | Tells us the number of standard deviations above or below the mean |
| Normal distribution | A model for quantitative data that often appears in the real world. Bell curve and symmetric. Determined by the mean(μ) and the standard deviation (σ) |
| Within 1 SD of the mean | About 68% of the data |
| Within 2 SD of the mean | About 95% of the data |
| Within 3 SD of the mean | About 99.7% of the data |
| Empirical Rule | 68-95-99.7 Rule |
| Density Curve | 1. Area under the curve is always 1 2. The entire curve is above the x-axis |
| To find the percent of data values in a given interval for a normal distribution | Calculate a z-score and then use Table A or calculator normalCDF |
| How can we use the z-score to find the percent of data values (left, right, between) | Left: get area from Table A Right: 1-area from Table A Between: subtract two areas from Table A. |
| How can we find the value, given an area (proportion) for a normal distribution? | Use Table A to find z-score Set up equation and solve |
| How do you get a z-score on the calculator? | Press 2nd → VARS (that’s DISTR). Choose 2:normalcdf (to find area/probability) or 2:invNorm (to find z from percentile). If finding just z: you usually calculate manually with formula. |
| How do you use the calculator to find the probability of being between two z-scores? | normalcdf(lower z, upper z) Example: P(-1 < Z < 2) = normalcdf(-1, 2) → about 0.82. |
| What does invNorm do on the calculator? | Find the z-score (or x-value) for a given percentile. Example: 90th percentile → invNorm(0.90) ≈ 1.28. |
| Graphical representation | displays data visually using charts, graphs, and diagrams |
| Numerical representation | uses raw numbers and tables |
| Equation of a line of best fit | y=a+bx |
| Coefficient of determination (R²) | A between 0 and 1 measures how well a statistical model predicts an outcome |
| Correlation coefficient (r) | A number between -1 and 1 that measures the strength and direction of the relationship between two variables |
| Side-by-Side Bar Chart | A visual tool used to compare different categories or groups |
| Segmented Bar Chart | Used to visualize data segments within bars for comparison across categories |
| Mosaic plot | A special type of stacked bar chart that shows percentages of data in groups. |
| Standard Normal Distribution | A normal distribution with a mean of 0 and a standard deviation of 1. Results when any normal curve is converted to standardized scores and is written as: Z~N(0,1) |
| Explanatory variable | Attempts to explain/influence changes in another variable. Different values of this variable are called treatments |
| Response variable | Affected variable, what is changed by altering the explanatory variables. |
| What does N(μ,σ) represent in statistics? | It represents a normal distribution with a mean of μ and a standard deviation of σ |
| What is the objective when we are given two normal distributions, N(μ1,σ1) and N(μ2,σ2), and asked to find a linear transformation y=a+bx? | The goal is to find the constants "a" (the y-intercept) and "b" (the slope) such that if a random variable x follows N(μ1,σ1), then the transformed variable y=a+bx follows N(μ2,σ2), |
| Given N(18,2) transforms to N(70,6), how do we find "b"? | Use the standard deviation relationship: σ2=b x σ1. Here 6=b x 2 Solving for b, we get b=6/2=3 |
| How do we find "a" if b=3 and the means from N(18,2) and N(70,6) | Use the mean relationship: μ2=a+b x μ1 . Here, 70=a+3 x 18. Solving for a, we get a=70-54=16 |
| Positive | As x values increase, the y values also tend to increase |
| Negative | As x values increase, the y-values tend to decrease |
| Strong | Data closely follow the pattern (e.g. linear) |
| Weak | Data doesn't closely follow the pattern (e.g. linear) |
| Population | An entire group that you want to draw conclusions about in a study |
| Sample | A smaller, manageable group selected from the population to represent it. |
| Population Distribution | A display of the frequency of each value in the entire population |
| Sample Distribution | A display of the frequency of each value in a sample taken from the population |
| What does N(x̄,Sx ) represent in statistics? | It represents a normal distribution with a mean of x̄ and a standard deviation of Sx |
| μ (mu) | Mean or average of a population |
| σ (sigma) | Standard deviation of a population |
| Percentages/ percentiles in a curve | 0.15%, 2.35%, 13.5%, 34%, 34%, 13.5%, 2.35%, 0.15% |
| Approx. Normal | Min/ Max need to be about 2-3 SD away from the mean |
| Normal CDF | (lower bound, upper bound, mean, SD)=% |
| Inv Norm | (area as %, mean, SD)=gives data value pr z-score |
| Calculate a z-score | z = (x-μ)/σ or z= (x-x̄)/SD |
| Percentile | % at the value and lower |
| Negative r value | negative correlation |
| Positive r value | positive correlation |
| Assigning if Data is Approx. Normal: | Summary Statistics (68-95-99.7 Rule) Graphically (normal probability plot) |
| Showing your work | 1. Identify the distribution: This could be N(μ,σ) for a general normal distribution or N(0,1) for a standard normal distribution. 2. Convert z-score: using z = (x-μ)/σ or z= (x-x̄)/SD 3.Use Table or Calculator 4. State the answer |
| Calculator Normal CDF | (low,up,mu,sigma) |
| The sign of the correlation coefficient (r) | Tells you the direction of a linear relationship |
| The magnitude of the correlation coefficient (r) | quantifies the strength of a linear relationship |
| The correlation coefficient (r) alone | doesn't provide enough information to make claims about form or unusual features in a relationship |
| Correlation | doesn't equal causation |
Created by:
Leo12345
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