AP Stats Interpretations For Final 1/15

z-score

specific value with context is z-score standard deviations above/below the mean.

Example: A quiz score of 71 is 1.43 standard deviations below the mean (z = -1.43).

percentile

percentile % of context are less than or equal to value.

Example: 75% of high school student SAT scores are less than or equal to 1200.

correlation ( r )

the linear association between x-context and y-context is weak/moderate/strong (strength) and positive/negative (direction)

Example: The linear association between student absences and final grades is fairly strong and negative (r=-0.93).

describing a distribution

address shape, center, variability, and outliers (in context)

Example: The distribution of student height is unimodal and roughly symmetric. The mean height is 65.3 inches with a standard deviation of 8.2 inches. There is a potential upper outlier at 79 inches and a gap between 60 and 62 inches.

residual

the actual y-context was residual above/below the predicted value when x-context = #.

Example: The actual heart rate was 4.5 beats per minute above the number predicted when Matt ran for 5 minutes.

y-intercept

the predicted y-context when x = 0 context is y-intercept.

Example: The predicted time to checkout at the grocery store when there are 0 customers in line is 72.95 seconds.

slope

the predicted y-context increases/decreases by slope for each additional x-context.

Example: The predicted heart rate increases by 4.3 beats per minute for each additional minute jogged.

standard deviation of residuals (s)

the actual y-context is typically about s away from the value predicted by the LSRL.

Example: The actual SAT score is typically about 14.3 points away from the value predicted by the LSRL.

coefficient of determination (r²)

about r²% of the variation in y-context can be explained by the linear relationship with x-context.

Example: About 87.3% of variation in electricity production is explained by the linear relationship with wind speed.

when is a linear model appropriate?

a linear model is appropriate when the relationship between variables appears as a straight line on a scatter plot and the data points form a random scatter around zero on a residual plot (no curve/pattern).

WORD IT LIKE THIS: The absence of any trends or patterns indicates that a linear model is appropriate.

describing the relationship

be sure to address strength, direction, form, and unusual features (in context).

Example: The scatterplot reveals a moderately strong, positive, linear association between the weight and length of rattlesnakes. The point at (24.1, 35.7) is a potential outlier.

expected value (mean, μ)

if the random process of context is repeated a very large number of times, the average number of x-context we can expect is expected value.

Example: If the random process of asking a student how many movies they watched this week is repeated a very large number of times, the average number of movies we can expect is 3.23 movies.

binomial mean (μX)

after many, many trials, the average number of success context out of n is μX.

Example: After many, many trials, the average number of property crimes that go unsolved out of 100 is 80.

binomial standard deviation (σX)

The number of success context out of n typically varies by σX from the mean of μX.

Example: The number of property crimes that go unsolved out of 100 typically varies by 1.6 crimes from the mean of 80 crimes.