Q1. Construct a frequency distribution with seven classes for the out-of-pocket prescription medicine expenses (in dollars) for 30 U.S. adults.

Background

Topic: Frequency Distributions

This question tests your ability to organize raw quantitative data into a frequency distribution table, which is a fundamental skill in descriptive statistics.

Key Terms and Formulas:

• Frequency Distribution: A table that shows how data are distributed across different intervals (classes).

• Class Width:

• Range:

Step-by-Step Guidance

1. Find the minimum and maximum values in the data set.

2. Calculate the range using .

3. Determine the class width by dividing the range by the number of classes (7), then round up if necessary.

4. Set up the class limits, starting from the minimum value, and create seven classes using the class width.

5. Count how many data points fall into each class to fill in the frequency column.

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Q2. Use a stem-and-leaf plot to display the number of hours 24 nurses worked last week. Describe any patterns.

Background

Topic: Stem-and-Leaf Plots

This question tests your ability to organize and visualize quantitative data using a stem-and-leaf plot, which helps identify patterns and distribution shapes.

Key Terms and Formulas:

• Stem-and-Leaf Plot: A graphical method for displaying data where each data value is split into a "stem" (leading digit(s)) and a "leaf" (trailing digit).

Step-by-Step Guidance

1. Sort the data from smallest to largest.

2. Identify the stems (typically the tens place) and leaves (ones place) for each value.

3. List the stems in a column, and write the leaves next to each stem in order.

4. Check for any patterns, such as clustering or gaps, in the plot.

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Q3. Use a pie chart to organize the number of earned degrees conferred (in thousands) in 2014: Associate’s (1003), Bachelor’s (1870), Master’s (754), Doctoral (178).

Background

Topic: Pie Charts

This question tests your ability to represent categorical data as proportions of a whole using a pie chart.

Key Terms and Formulas:

• Pie Chart: A circular chart divided into sectors, each representing a category's proportion.

• Percent of Total:

Step-by-Step Guidance

1. Calculate the total number of degrees conferred by summing all categories.

2. For each category, compute its percentage of the total using the formula above.

3. Draw a circle and divide it into sectors according to the calculated percentages.

4. Label each sector with the degree type and its percentage.

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Q4. Use a Pareto chart to organize the leading causes of death in the United States in 2014. What was the leading cause?

Background

Topic: Pareto Charts

This question tests your ability to organize categorical data by frequency in descending order using a Pareto chart.

Key Terms and Formulas:

• Pareto Chart: A bar graph where categories are ordered from highest to lowest frequency.

Step-by-Step Guidance

1. List each cause of death and its frequency.

2. Order the causes from highest to lowest frequency.

3. Draw a bar graph with categories on the x-axis and frequencies on the y-axis.

4. Identify the tallest bar as the leading cause.

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Q5. Graph the lengths of employment and salaries of 10 employees using a scatter plot. Describe any trends.

Background

Topic: Scatter Plots

This question tests your ability to visualize the relationship between two quantitative variables using a scatter plot.

Key Terms and Formulas:

• Scatter Plot: A graph that plots pairs of values (x, y) to show possible correlation.

• Trend: The general direction in which data points move (positive, negative, or no correlation).

Step-by-Step Guidance

1. List each employee’s length of employment (x-axis) and salary (y-axis).

2. Plot each pair as a point on the scatter plot.

3. Observe the pattern of points to see if there is a trend (e.g., do higher years correspond to higher salaries?).

4. Describe the trend: positive, negative, or no correlation.

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Q6. Construct a time series chart for the number of motor vehicle thefts (in millions) in the United States from 2005 to 2015. Describe any trends.

Background

Topic: Time Series Charts

This question tests your ability to visualize data over time and identify trends.

Key Terms and Formulas:

• Time Series Chart: A graph that plots data points over time to show trends.

Step-by-Step Guidance

1. List the years and corresponding motor vehicle theft numbers.

2. Plot the years on the x-axis and theft numbers on the y-axis.

3. Connect the points to show the trend over time.

4. Observe whether the numbers are increasing, decreasing, or stable.

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Q7. What is the mean weight of the adults before starting a weight-loss study?

Background

Topic: Measures of Central Tendency (Mean)

This question tests your ability to calculate the arithmetic mean of a data set.

Key Terms and Formulas:

• Mean:

• = sum of all data values

• = number of data values

Step-by-Step Guidance

1. Add up all the weights given in the data set.

2. Count the number of adults in the sample.

3. Divide the total sum by the number of adults to find the mean.

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Q8. Find the mean, median, and mode of the sample ages of students in a class. Are there any outliers? Which measure best describes a typical entry?

Background

Topic: Measures of Central Tendency and Outliers

This question tests your ability to compute mean, median, mode, and identify outliers in a data set.

Key Terms and Formulas:

• Mean:

• Median: The middle value when data is ordered.

• Mode: The value that appears most frequently.

• Outlier: A value much higher or lower than most others.

Step-by-Step Guidance

1. Order the ages from smallest to largest.

2. Calculate the mean by summing all ages and dividing by the number of students.

3. Find the median by locating the middle value(s).

4. Identify the mode by finding the most frequent age.

5. Check for outliers (e.g., the age 65) and consider which measure best represents the data.

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Q9. Determine your grade point average (weighted mean) using the grades and credit hours provided.

Background

Topic: Weighted Mean

This question tests your ability to calculate a weighted mean, which is used for GPA calculations.

Key Terms and Formulas:

• Weighted Mean:

• = weight (credit hours), = grade points

Step-by-Step Guidance

1. Assign grade points to each grade (A=4, B=3, C=2, D=1, F=0).

2. Multiply each grade point by its credit hours.

3. Add up all the products and divide by the total credit hours.

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Q10. Calculate your English average using your scores and weights: Tests (82, 70%), Quizzes (91, 20%), Participation (95, 10%).

Background

Topic: Weighted Mean

This question tests your ability to calculate a weighted average for grades.

Key Terms and Formulas:

• Weighted Mean: (if weights sum to 1 or 100%)

Step-by-Step Guidance

1. Convert the weights to decimals (e.g., 70% = 0.70).

2. Multiply each score by its weight.

3. Add the weighted scores to get the average.

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Q11. Estimate the mean expense using the frequency distribution for out-of-pocket prescription medicine expenses. Compare with the sample mean .

Background

Topic: Mean of Grouped Data

This question tests your ability to estimate the mean from a frequency distribution.

Key Terms and Formulas:

• Estimated Mean:

• = frequency, = class midpoint

Step-by-Step Guidance

1. Multiply each class midpoint by its frequency.

2. Add up all the products.

3. Divide the sum by the total frequency (number of data points).

4. Compare the estimated mean to the sample mean.

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Q12. Find the population variance and standard deviation of the starting salaries for Lockheed Martin (in 1000s).

Background

Topic: Population Variance and Standard Deviation

This question tests your ability to calculate variance and standard deviation for a population.

Key Terms and Formulas:

• Population Variance:

• Population Standard Deviation:

• = population mean, = number of values

Step-by-Step Guidance

1. Find the mean () of the salaries.

2. Subtract the mean from each salary and square the result.

3. Add up all the squared differences.

4. Divide by to get the variance.

5. Take the square root of the variance to get the standard deviation.

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Q13. Find the sample variance and standard deviation of recovery times (in days) for Group 1 football players.

Background

Topic: Sample Variance and Standard Deviation

This question tests your ability to calculate variance and standard deviation for a sample.

Key Terms and Formulas:

• Sample Variance:

• Sample Standard Deviation:

• = sample mean, = sample size

Step-by-Step Guidance

1. Find the sample mean () of the recovery times.

2. Subtract the mean from each value and square the result.

3. Add up all the squared differences.

4. Divide by to get the variance.

5. Take the square root to get the standard deviation.

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Q14. Estimate the percent of women whose heights are between 58.4 inches and 64.2 inches, given mean 64.2 and standard deviation 2.9.

Background

Topic: Empirical Rule (68-95-99.7 Rule)

This question tests your ability to use the Empirical Rule to estimate percentages within standard deviations of the mean.

Key Terms and Formulas:

• Empirical Rule: For a normal distribution, about 68% of values fall within 1 standard deviation of the mean.

Step-by-Step Guidance

1. Calculate how many standard deviations 58.4 is below the mean:

2. Determine the percentage of data between and using the Empirical Rule.

3. Recall that about 34% of data falls between and , and another 13.5% between $\mu - 1\sigma$ and .

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Q15. Using Chebyshev’s Theorem, determine at least how many of the 40 households have 0 to 4 pets, given mean 2 and standard deviation 1.

Background

Topic: Chebyshev’s Theorem

This question tests your ability to use Chebyshev’s Theorem to estimate the minimum proportion of data within a certain number of standard deviations.

Key Terms and Formulas:

• Chebyshev’s Theorem: At least of the data lies within standard deviations of the mean.

• (since 0 to 4 is 2 units from the mean)

Step-by-Step Guidance

1. Calculate as the number of standard deviations from the mean to the endpoints.

2. Apply Chebyshev’s formula: .

3. Multiply the result by the total number of households to find the minimum number.

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Q16. Estimate the sample mean and sample standard deviation from the frequency distribution of travel expenses.

Background

Topic: Mean and Standard Deviation of Grouped Data

This question tests your ability to estimate mean and standard deviation from grouped data.

Key Terms and Formulas:

• Estimated Mean:

• Estimated Standard Deviation:

• = frequency, = class midpoint

Step-by-Step Guidance

1. Multiply each class midpoint by its frequency and sum the products.

2. Divide by the total frequency to estimate the mean.

3. For standard deviation, subtract the mean from each midpoint, square the result, multiply by frequency, sum, and divide by .

4. Take the square root to estimate the standard deviation.

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Q17. Find the coefficient of variation for the heights and weights of a basketball team. Compare the results.

Background

Topic: Coefficient of Variation

This question tests your ability to compare variability between two data sets using the coefficient of variation.

Key Terms and Formulas:

• Coefficient of Variation:

• = standard deviation, = mean

Step-by-Step Guidance

1. Calculate the mean and standard deviation for heights.

2. Calculate the mean and standard deviation for weights.

3. Compute the coefficient of variation for each using the formula above.

4. Compare which data set has greater relative variability.

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Q18. Find the five-number summary for the gallons of fuel wasted by commuters in the 15 largest U.S. urban areas.

Background

Topic: Five-Number Summary

This question tests your ability to find the minimum, Q1, median, Q3, and maximum values in a data set.

Key Terms and Formulas:

• Five-Number Summary: Minimum, Q1, Median, Q3, Maximum

• Quartiles: Values that divide the data into four equal parts.

Step-by-Step Guidance

1. Order the data from smallest to largest.

2. Identify the minimum and maximum values.

3. Find the median (middle value).

4. Find Q1 (median of lower half) and Q3 (median of upper half).

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Q19. Find the z-score for each speed measured (62, 47, 56 mph) given mean 56 mph and standard deviation 4 mph.

Background

Topic: Z-Scores

This question tests your ability to standardize values using z-scores.

Key Terms and Formulas:

• Z-Score:

• = value, = mean, = standard deviation

Step-by-Step Guidance

1. Subtract the mean from each speed.

2. Divide the result by the standard deviation to get the z-score.

3. Repeat for each speed.

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