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If a value k is added to every element in a data set, how does this affect measures of center (mean, median, mode)?
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If a value k is multiplied to every element in a data set, how does this affect measures of center (mean, median, mode)?
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ap stats questions
51-101
| Question | Answer |
|---|---|
| If a value k is added to every element in a data set, how does this affect measures of center (mean, median, mode)? | +/- k to measures of center |
| If a value k is multiplied to every element in a data set, how does this affect measures of center (mean, median, mode)? | multiply/divide k to measures of center |
| If a value k is added to every element in a data set, how does this affect measures of spread (range, IQR, standard deviation)? | no change to measures of spread |
| If a value k is multiplied to every element in a data set, how does this affect measures of spread (range, IQR, standard deviation)? | multiply/divide k to measures of spread variance: multiply/divide k^2 |
| What is the Central Limit Theorem? | ensures sampling distribution will be approximately normal despite the population distribution as sample size increases: shape becomes more normal, spread is smaller, and t* approaches z* |
| What is the Law of Large Numbers? | if we observe more repetitions of any chance process, the proportion of times a specific outcome occurs approaches a single value (true mean) as the number of samples increases, the center approaches the true mean |
| What is the Empirical Rule? When does this apply? | 68% of data falls within 1 std, 95% of data falls within 2 std , and 99.7% of data falls within 3 std only applies if data is normally distributed and z-scores are clean numbers (-3,-2,-1,0,1,2,3) |
| How does the mean and median compare in a graph that is symmetric? Skewed right? Skewed left? | symmetric: mean and median in middle skewed right: mean close to peak of curve but pulled right median peak of curve skewed left: mean close to peak but pulled left median peak of curve |
| What is the difference between bivariate vs univariate data? | bivariate: 2 variables univariate: 1 variable |
| How are univariates displayed? Bivariates? | univariates: displays that only use 1 category (histogram, bar graph, pie chart, dot plot, box plot, box and whisker) bivariate: displays that use 2 categories (2 way table, venn diagram, xy graph) |
| What is the explanatory variable? Response variable? | explanatory response variable: cause, variable that can be manipulated to change the response variable, x response variable: predicted response, variable affected by explanatory response variable, y |
| What is the LSRL? Define all variables. | y-hat = a+bx y-hat is the predicted response variable x is the explanatory variable definition |
| What is the meaning of "least squares"? | minimizes sum of residuals squared of all observations from the prediction line |
| What does the slope mean in the context of a problem? | For every x, y is predicted to increase/decrease by ??? |
| What does the y-intercept mean in the context of a problem? | If x is 0, y is expected to be y-intercept |
| What is r called? What does it mean in the context of a problem? | There is a strong/mild/weak positive/negative linear relationship between x and y. This is the correlation coefficient. |
| What is r^2 called? What does it mean in the context of the problem? | ??? of the variability of y is due to x. This is the coefficient of determination. |
| What happens to the value of r if you switch the x and y variables? | r does not change |
| What happens to the value of r if you add a constant value to each response value? | r does not change |
| What happens to the value of r if you multiply a constant value to each response value? | r does not change |
| What happens to the value of r if you change the unit of measure? | r does not change |
| What are the possible values of r? | r ranges from -1 to 1 |
| If r=0.3, what does that indicate about the association of your data set? | There is a weak, positive linear relationship between x and y |
| If r=-0.9 what does that indicate about the association of your data set? | There is a strong, negative linear relationship between x and y |
| How does r differ from the slope of the LSRL? | r measures the strength of linear relationship slope measures how much the y will change when x changes by 1 |
| How do you extract LSRL from a computer printout? | using y-hat = a + bx use 1st number under coef for a use the 2nd number under coef for b |
| How do you find the t-score from a computer printout? | take the coeff of x and divide it by the standard deviation |
| How does an outlier/influential point affect r, r^2, and the slope of a line? | OUTLIER r: artificially reduces r^2: artificially reduces slope: pulls toward outlier INFLUENTIAL POINT r: artificially inflates r^2: artificially inflates slope: pulls toward influential point |
| How can you determine if a line is a good fit for a set of data? | residual plot randomly distributed r^2, higher the better |
| What is the formula that involved slope, correlation, and standard deviation? | b = r (sy/sx) b: slope r: correlation coefficient sy and sx: standard deviation of y and x |
| What point is always on any LSRL? | (x bar, y bar) x bar: mean of x y bar: mean of y |
| What does resistant and non resistant mean? | resistant: outliers do not greatly affect value median, mode, IQR, Q1, Q3 non resistant: outliers greatly affect value mean, standard deviation, range, r, r^2 |
| What is s on the Minitab printout? | root square mean error standard deviation of residuals |
| What is a residual? | difference between observed and predicted value |
| What is a residual plot? | scatter plot of residuals compared to the regression line assess how well a regression line fits the data |
| If a residual is positive, how does your model compare with the actual value? | predicted underestimates actual |
| If a residual is negative, how does your model compare with the actual value? | predicted overestimates actual |
| If an observed point is above LSRL, is the residual positive or negative? | positive |
| If an observed point is below LSRL, is the residual positive or negative? | negative |
| What is the sum of all residuals (of an LSRL)? | 0 |
| What is the difference between interpolation and extrapolation? | interpolation: estimation of values between known data points extrapolation: estimation of values beyond known data points |
| What is the difference between correlation and causation? | correlation: measure of strength and direction of relationship between 2 variables causation: how one variable affects another |
| What are two other ways an association/correlation can occur? | common response confounding response |
| What is a common response? | changes in x and y are caused by changes in a lurking variable |
| What is a confounding response? | possibility that change in x is causing change in y OR change in lurking variable causes change in y |
| What is the difference between a parameter and statistic? | parameter: describes the whole population statistic: describes a sample |
| What is the difference between bias and variability? | bias: center of sampling distribution does NOT equal true value of parameter, aiming variability: spread of sampling distribution, consistency |
| What is the best way to minimize both bias and variability? | increase sample size |
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