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Describing data and best-fit lines exercises · Physics Playground

Describing data and best-fit lines

53 problems with worked solutions, from Statistics.

Start with a random one

Learn it first: Measurement & Uncertainty, Best-Fit Lines & Straightening Curves

Statistics1.1 Definitions of Statistics, Probability, and Key Terms

Example 1.1Determine what the population, sample, parameter, statistic, variable, and data referred to in the following study. We want to know the mean amount of extracurricular activities in which high school students…
Example 1.2Determine what the key terms refer to in the following study. A study was conducted at a local high school to analyze the average cumulative GPAs of students who graduated last year. Fill in the letter of the phrase…
Example 1.3Determine what the population, sample, parameter, statistic, variable, and data referred to in the following study. As part of a study designed to test the safety of automobiles, the National Transportation Safety…
Example 1.4Determine what the population, sample, parameter, statistic, variable, and data referred to in the following study. An insurance company would like to determine the proportion of all medical doctors who have been…

Statistics1.2 Data, Sampling, and Variation in Data and Sampling

Example 1.7Name data sets that are quantitative discrete, quantitative continuous, and qualitative.
Example 1.9Work collaboratively to determine the correct data type: quantitative or qualitative. Indicate whether quantitative data are continuous or discrete. Hint: Data that are discrete often start with the words the number…
Example 1.10A statistics professor collects information about the classification of her students as freshmen, sophomores, juniors, or seniors. The data she collects are summarized in the pie chart Figure 1.3. What type of data…With a figure
Example 1.11Suppose the guidance counselors at De Anza and Foothill need to make an oral presentation of the student data presented in Figures 1.5 and 1.6. Under what context should they choose to display the pie graph? When…
Example 1.12A study is done to determine the average tuition that private high school students pay per semester. Each student in the following samples is asked how much tuition he or she paid for the fall semester. What is the…
Example 1.13Determine the type of sampling used (simple random, stratified, systematic, cluster, or convenience). A soccer coach selects six players from a group of boys aged eight to ten, seven players from a group of boys aged…
Example 1.14 (part 1)a. Do you think that either of these samples is representative of (or is characteristic of) the entire 10,000 part-time student population?
Example 1.14 (part 2)b. Since these samples are not representative of the entire population, is it wise to use the results to describe the entire population?
Example 1.14 (part 3)c. Is the sample biased?

Statistics1.3 Frequency, Frequency Tables, and Levels of Measurement

Example 1.15From Table 1.15, find the percentage of heights that are less than 65.95 inches.
Example 1.16From Table 1.15, find the percentage of heights that fall between 61.95 and 65.95 inches.
Example 1.17Use the heights of the 100 male semiprofessional soccer players in Table 1.15. Fill in the blanks and check your answers. The percentage of heights that are from 67.95–71.95 inches is ________. The percentage of…
Example 1.18Is the table correct? If it is not correct, what is wrong? True or False: Three percent of the people surveyed commute three miles. If the statement is not correct, what should it be? If the table is incorrect, make…
Example 1.19Answer the following questions: What is the frequency of deaths measured from 2006 through 2009? What percentage of deaths occurred after 2009? What is the relative frequency of deaths that occurred in 2003 or…

Statistics1.4 Experimental Design and Ethics

Example 1.20Researchers want to investigate whether taking aspirin regularly reduces the risk of a heart attack. 400 men between the ages of 50 and 84 are recruited as participants. The men are divided randomly into two groups:…
Example 1.21The Smell & Taste Treatment and Research Foundation conducted a study to investigate whether smell can affect learning. Subjects completed mazes multiple times while wearing masks. They completed the pencil and paper…
Example 1.22A researcher wants to study the effects of birth order on personality. Explain why this study could not be conducted as a randomized experiment. What is the main problem in a study that cannot be designed as a…
Example 1.23Describe the unethical behavior in each example and describe how it could impact the reliability of the resulting data. Explain how the problem should be corrected. A researcher is collecting data in a community. She…

Statistics2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs

Example 2.2Do the data seem to have any concentration of values? The leaves are to the right of the decimal.
Example 2.3A side-by-side stem-and-leaf plot allows a comparison of the two data sets in two columns. In a side-by-side stem-and-leaf plot, two sets of leaves share the same stem. The leaves are to the left and the right of the…
Example 2.5By the end of 2011, a social media site had more than 146 million users in the United States. Table 2.9 shows three age-groups, the number of users in each age-group, and the proportion (percentage) of users in each…
Example 2.6The columns in Table 2.11 contain the race or ethnicity of students in U.S. public schools for the class of 2011, percentages for the Advanced Placement (AP) examinee population for that class, and percentages for…
Example 2.7Table 2.13 is a two-way table showing the types of pets owned by men and women. Dogs Cats Fish Total Men 4 2 2 8 Women 4 6 2 12 Total 8 8 4 20 Table 2.13 Given these data, calculate the marginal distributions of pets…
Example 2.8Table 2.14 is a two-way table showing the types of pets owned by men and women. Dogs Cats Fish Total Men 4 2 2 8 Women 4 6 2 12 Total 8 8 4 20 Table 2.14 Given these data, calculate the conditional distributions for…

Statistics2.2 Histograms, Frequency Polygons, and Time Series Graphs

Example 2.10Calculate the width of each bar/bin size/interval size.
Example 2.11Using this data set, construct a histogram. Number of Hours My Classmates Spent Playing Video Games on Weekends 9.95 10 2.25 16.75 0 19.5 22.5 7.5 15 12.75 5.5 11 10 20.75 17.5 23 21.9 24 23.75 18 20 15 22.9 18.8…
Example 2.14The following data show the Annual Consumer Price Index each month for 10 years. Construct a time series graph for the Annual Consumer Price Index data only. YearJanFebMarAprMayJunJul 2003 181.7183.1184.2183.8…

Statistics2.3 Measures of the Location of the Data

Example 2.15For the following 13 real estate prices, calculate the IQR and determine if any prices are potential outliers. Prices are in dollars. 389,950; 230,500; 158,000; 479,000; 639,000; 114,950; 5,500,000; 387,000; 659,000;…
Example 2.17Using Table 2.24: Find the 80th percentile. Find the 90th percentile. Find the first quartile. What is another name for the first quartile?
Example 2.18Listed are 29 ages for Academy Award-winning best actors in order from smallest to largest: 18, 21, 22, 25, 26, 27, 29, 30, 31, 33, 36, 37, 41, 42, 47, 52, 55, 57, 58, 62, 64, 67, 69, 71, 72, 73, 74, 76, 77 Find the…
Example 2.20On a timed math test, the first quartile for time it took to finish the exam was 35 minutes. Interpret the first quartile in the context of this situation.
Example 2.21On a 20-question math test, the 70th percentile for number of correct answers was 16. Interpret the 70th percentile in the context of this situation.
Example 2.22At a high school, it was found that the 30th percentile of number of hours that students spend studying per week is seven hours. Interpret the 30th percentile in the context of this situation.

Statistics2.4 Box Plots

Example 2.25Find the smallest and largest values, the median, and the first and third quartile for Mr. Ramirez's class. Find the smallest and largest values, the median, and the first and third quartile for Ms. Park's class. For…

Statistics2.5 Measures of the Center of the Data

Example 2.27Data indicating the number of months a patient with a specific disease lives after taking a new antibody drug are as follows (smallest to largest): 3, 4, 8, 8, 10, 11, 12, 13, 14, 15, 15, 16, 16, 17, 17, 18, 21, 22,…
Example 2.28Suppose that in a small town of 50 people, one person earns $5,000,000 per year and the other 49 each earn $30,000. Which is the better measure of the center: the mean or the median?
Example 2.29Find the mode.
Example 2.31A frequency table displaying Professor Blount’s last statistic test is shown. Find the best estimate of the class mean. Grade Interval Number of Students 50–56.5 1 56.5–62.5 0 62.5–68.5 4 68.5–74.5 4 74.5–80.5 2…

Statistics2.6 Skewness and the Mean, Median, and Mode

Example 2.32Statistics are used to compare and sometimes identify authors. The following lists show a simple random sample that compares the letter counts for three authors. Terry: 7, 9, 3, 3, 3, 4, 1, 3, 2, 2 Davis: 3, 3, 3, 4,…

Statistics2.7 Measures of the Spread of the Data

Example 2.33For the following problems, recall that value = mean + (#ofSTDEVs)(standard deviation). Verify the mean and standard deviation on a calculator or computer. Note that these formulas are derived by algebraically…
Example 2.34Use the following data (first exam scores) from Susan Dean's spring precalculus class: 33, 42, 49, 49, 53, 55, 55, 61, 63, 67, 68, 68, 69, 69, 72, 73, 74, 78, 80, 83, 88, 88, 88, 90, 92, 94, 94, 94, 94, 96, 100…
Example 2.36Two students, John and Ali, from different high schools, wanted to find out who had the highest GPA when compared to his school. Which student had the highest GPA when compared to his school? Student GPA School Mean…

Statistics12.1 Linear Equations

Example 12.3Find the equation that expresses the total cost in terms of the number of hours required to complete the job.
Example 12.4What are the independent and dependent variables? What is the y-intercept, and what is the slope? Interpret them using complete sentences.

Statistics12.4 Prediction (Optional)

Example 12.10 (part 1)a. What would you predict the final exam score to be for a student who scored a 66 on the third exam?
Example 12.10 (part 2)b. What would you predict the final exam score to be for a student who scored a 90 on the third exam?

Statistics12.5 Outliers

Example 12.11In the third exam/final exam example, you can determine whether there is an outlier. If there is an outlier, as an exercise, delete it and fit the remaining data to a new line. For this example, the new line ought to…
Example 12.12Using this new line of best fit (based on the remaining 10 data points in the third exam/final exam example), what would a student who receives a 73 on the third exam expect to receive on the final exam? Is this the…
Example 12.13Draw a scatter plot of the data. Calculate the least-squares line. Write the equation in the form ŷ = a + bx. Draw the line on a scatter plot. Find the correlation coefficient. Is it significant? What is the average…