A.P. Statistics:Semester 1 ReviewJanuary 2015

Exam Breakdown

Part 1 – Displaying and summarizing categorical and quantitative data

Part 2 – Association, correlation, and data re-expression

Part 3 – Samples, surveys, experiments, and observations

Part 4 – Probability

Part 1: Chapters 1-6

Ch. 1 – 3: Displaying and describing categorical data Some vocabulary:

Categorical data, quantitative data, (relative) frequency table, (relative frequency) bar chart, pie chart, contingency table, marginal distribution, conditional distribution, segmented bar chart

Examples

A teacher surveyed his 88 students to see what their post-high school plans were. The results are in the contingency table below:

Male Female Total

Four-Year 22 18 40

Community 25 14 39

Workforce 4 5 9

Total 51 37 88

1. What is the marginal distribution for post-high school plans?2. What is the marginal distribution for gender?3. What percentage of males are going to a four-year college?4. What percentage of students going into the workforce are

females?

Part 1: Chapters 1-6

Ch. 4 – 5: Displaying and describing quantitative data Some vocabulary:

Histogram, gap, stem-and-leaf display, dotplot, shape-center-spread, unimodal/bimodal, uniform, symmetric, skewed, (far) outliers, median, range, IQR, mean, 5-number summary, boxplot

Examples

Draw a stem-and-leaf plot for the following data set:

2 2 6 7 9 13 13 15 16 1818 19 22 23 25 26 26 31 34

What is an advantage of making a stem-and-leaf display?

Examples

Draw a boxplot for the following data set (include the imaginary fences and identify any outliers).

2 2 6 7 9 13 13 15 16 1818 19 22 23 25 26 26 31 34

Examples

During finals week at a local college, 48 students studied for a total of 14 hours and 67 students studied for a total of 22 hours for their psychology exam. Overall, what was the mean number of hours spent studying of all the students in this psychology class?

Part 1: Chapters 1-6

Ch. 6: Normal Distribution Some vocabulary:

Standardizing, z-score, shifting, rescaling, standard deviation, normal model, parameter, statistic, 68-95-99.7 Rule

Calculator skills to know: Normalcdf – when you are trying to find percentages

Invnorm – when you are trying to find cut-off points (you are given the percentages)

Examples

Sarah and Emma are in AP Calculus at the same school but have the class with different teachers. Sarah scored an 84% on her final exam and her class’ average was a 73% with a standard deviation of 8%. Emma scored a 92% on her final exam and her class’ average was an 81% with a standard deviation of 14%. Assuming the scores on each exam were approximately normally distributed, who did relatively better on the final exam?

Examples

Suppose that the distribution of a set of scores has a mean of 33 and a standard deviation of 7.

1. If 5 is added to each score, what will be the mean and standard deviation of the new scores?

2. If each scores is multiplied by 3, what will be the mean and standard deviation of the new scores?

Examples

The average monthly rent for an apartment at the U of I is $456.00 with a standard deviation of $58.00. Assume the apartment prices are normally distributed.

1. Clearly draw and label the normal model

Examples

The average monthly rent for an apartment at the U of I is $456.00 with a standard deviation of $58.00. Assume the apartment prices are normally distributed.

2. What percentage of apartments cost more than $500.00?

Examples

The average monthly rent for an apartment at the U of I is $456.00 with a standard deviation of $58.00. Assume the apartment prices are normally distributed.

3. What percentage of apartments cost between $375.00 and $480.00?

Examples

The average monthly rent for an apartment at the U of I is $456.00 with a standard deviation of $58.00. Assume the apartment prices are normally distributed.

4. The cities of Champaign-Urbana want a $400 monthly rent to be the lower 10% of rent prices. Assume the mean rent price will stay the same, what standard deviation must they achieve?