Final Review 1 - Copy

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May 1, 2024

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AP Stats/Stats Fall Semester Final Review 1 (Chapter 1-3) Topic 1: Summary statistics for a quantitative variable Vocabulary: Symmetric distribution Left-skewed distribution Right-skewed distribution Mean Median Range Standard deviation IQR Outliers 1.5 ⨉ IQR rule Percentile Resistant measure 1. We will analyze these quiz scores from a 50-point quiz. Consider it a sample of quiz scores. 20 42 29 28 29 36 34 31 50 31 45 29 30 48 44 50 30 25 24 36 29 38 17 42 43 30 31 35 44 40 30 (a) Find the mean, median, standard deviation, IQR and range of the data set. (b) Based on the shape of the distribution, what measures of center and spread would be most appropriate? Explain. (c) Mathematically check for outliers using the 1.5 x IQR rule. (d) Describe the distribution of quiz scores. Remember use S.O.C.S. (e) Calculate the percentile rank for a quiz score of 31. Show your work. Topic 2: Graphical Display of Summary Stats and Comparing Distributions Vocabulary: 5-number summary Boxplot A class of 8th graders took a reading test and the scores are reported by reading grade level. The 5-number summaries for 18 males and 15 female students are shown below: Males: 6.0 7.9 8.3 8.9 10 Females: 6.8 7.8 8.5 9.2 9.9 (a) Which group had the highest score? (b) Which group had the greater range? (c) Which group had the greater interquartile range? (d) Which group’s scores are more skewed? (e) If the male’s mean score was 8.2 and for the females was 8.6, what is the overall mean for this class? (f) Create a parallel boxplots for the two groups. 1
AP Stats/Stats Fall Semester Final Review 1 (Chapter 1-3) Topic 3: The normal distribution and empirical rule. IQ scores are approximately normally distributed with a mean of 105 and a standard deviation of 15. Use the Standard Normal Table for questions a-e. (a) What percent of IQs would you expect to be over 90? Show your work. (b) What percent of IQs would you expect to be between 110 and 130? Show your work. (c) What percent of IQs would you expect to be under 100? Show your work. (d) What IQ represents the 25th percentile? (e) What IQ marks the top 5% of all IQs? Topic 4: Representing the relationship between two quantitative variables Vocabulary: Scatterplot Explanatory variable Response variable Positive association Negative association Residual The heights (inches) and shoe sizes (mens sizes) were collected from a random sample of 15 students at a certain high school. (a) Identify the explanatory variable. (b) Identify the response variable. (c) Construct a scatterplot. (d) Describe the relationship between the heights and shoe sizes. 2
AP Stats/Stats Fall Semester Final Review 1 (Chapter 1-3) Topic 5: Correlation (a) Calculate the correlation coe ffi cient (r) for our class data on knee height and overall height. (b) What does r tell us about the relationship between knee height and overall height? Determine if the following statements are true or false. If the statement is false, rewrite it as a true statement. (c) If your correlation coe ffi cient is close to 1 or -1, you have evidence that there is a linear relationship between the two variables. (d) If you were to change the measurements from centimeters to inches, the correlation coe ffi cient would not change (e) You can calculate the correlation coe ffi cient as long as one of your variables is quantitative. (f) If you switch your explanatory variable to the y-axis and the response variable to the x-axis, the correlation coe ffi cient will change. (g) Correlation only describes how strong a linear relationship is between two variables The correlation coe ffi cient is only mildly a ff ected by outlying observations. Topic 6: Linear regression Vocabulary: Least square regression line(LSRL) Predicted value of the LSRL Slope of the LSRL Y-intercept of the LSRL (a) Create the Least-Squares Regression Line. (b) Identify the slope and interpret it. (c) Identify the y-intercept and interpret it. (d) Predict the y value for an x value of 6. Show your work. (e) Should you use the LSRL to predict a “y” value for an “x” value of 19? Explain. 3
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