Interpret Data Displays - Praxis Core Math

1. A data table classifies 200 surveyed students by class year and whether they have a part-time job. The survey included 80 freshmen and 120 upperclassmen. Of the freshmen, 30 have a job. In total, 100 students surveyed have a job. Based on this information, which statement is true?
   Answer: More upperclassmen have a job than do not have a job. From the data: Total with jobs = 100. Freshmen with jobs = 30. Therefore, upperclassmen with jobs = 100 - 30 = 70. Total upperclassmen = 120. Therefore, upperclassmen without jobs = 120 - 70 = 50. Comparing these two numbers for upperclassmen, 70 have a job and 50 do not. So, more upperclassmen have a job than do not.
2. A line graph shows the outdoor temperature at various times. At 12:00 PM, the temperature was 70°F. By 10:00 PM, the temperature had dropped to 50°F. What was the average rate of change in temperature, in degrees Fahrenheit per hour, between 12:00 PM and 10:00 PM?
   Answer: A decrease of 2 degrees per hour Rate of change is the change in temperature divided by the change in time. The change in temperature is 50°F - 70°F = -20°F. The change in time is from 12:00 PM to 10:00 PM, which is 10 hours. The average rate of change is -20 degrees / 10 hours = -2 degrees per hour, which represents a decrease of 2 degrees per hour.
3. A researcher describes the scatterplot of two variables, X and Y, as 'a random cloud of points with no discernible upward or downward trend.' Which of the following correlation coefficients (r) would best describe the relationship shown in the plot?
   Answer: r = 0.03 The correlation coefficient (r) measures the strength and direction of a linear relationship. An r-value near +1 or -1 indicates a strong positive or negative linear relationship, respectively. An r-value near 0 indicates little to no linear relationship. A 'random cloud of points' describes a lack of correlation, so an r-value close to 0, like 0.03, is the best fit.
4. A table displays the quarterly sales figures (in thousands of dollars) for three products. Product A's sales were 100, 110, 130, and 150. Product B's sales were 50, 60, 80, and 90. Product C's sales were 200, 210, 220, and 250. Which product experienced the greatest percentage increase in sales from the first quarter to the fourth quarter?
   Answer: Product B To find the percentage increase, use the formula: ( (New Value - Old Value) / Old Value ) * 100. For Product A: ( (150 - 100) / 100 ) * 100 = 50%. For Product B: ( (90 - 50) / 50 ) * 100 = 80%. For Product C: ( (250 - 200) / 200 ) * 100 = 25%. Product B had the greatest percentage increase (80%).
5. A histogram of employee salaries at a large corporation shows that the majority of employees earn between $40,000 and $70,000. The bars on the histogram become progressively shorter for higher salary intervals, forming a long tail to the right. Which of the following statements is most likely true about the salaries?
   Answer: The mean salary is greater than the median salary. The description indicates a right-skewed distribution (skewed toward higher values). In a right-skewed distribution, the mean is pulled in the direction of the long tail (the higher salaries), making it greater than the median, which is more resistant to extreme values.
6. A double line graph displays the monthly visitors to Park A and Park B. In June, Park A had 1,500 visitors and Park B had 1,200. In July, Park A's visitors increased by 20%, while Park B had 1,600 visitors. In August, both parks had 1,800 visitors. In which month was the absolute difference in the number of visitors between the two parks the greatest?
   Answer: June Calculate the difference for each month. June: |1,500 - 1,200| = 300. July: Park A had 1,500 * 1.20 = 1,800 visitors. The difference was |1,800 - 1,600| = 200. August: |1,800 - 1,800| = 0. The greatest difference was 300, which occurred in June.
7. The five-number summary for a dataset is given as: Minimum = 20, Q1 = 50, Median = 65, Q3 = 80, Maximum = 150. Using the common definition of an outlier as a value more than 1.5 times the interquartile range (IQR) below Q1 or above Q3, which of the following statements is true?
   Answer: The maximum value is an outlier, but the minimum value is not. First, calculate the IQR: IQR = Q3 - Q1 = 80 - 50 = 30. Next, calculate the outlier threshold: 1.5 IQR = 1.5 30 = 45. The lower boundary for outliers is Q1 - 45 = 50 - 45 = 5. The upper boundary is Q3 + 45 = 80 + 45 = 125. The minimum value (20) is not below 5, so it is not an outlier. The maximum value (150) is above 125, so it is an outlier.
8. The two-way table below shows the number of adults surveyed about their preferred type of exercise, categorized by age group. Based on the table shown, among adults who prefer running, what percent are aged 18–29?
   Answer: 40% Adults who prefer running total: 40 + 35 + 25 = 100. Of these, 40 are aged 18–29. 40/100 = 40%. (A) 24% = 40/165 (using wrong denominator—total of age 18–29). (B) 30% = 40/135 (using total surveyed divided incorrectly). (D) 60% confuses the complement.
9. A line graph showing a company's annual profits from 2020 to 2023 displays the following data points: 2020 ($10 million), 2021 ($10.5 million), 2022 ($11.2 million), and 2023 ($12 million). The vertical axis of the graph is labeled starting at $10 million instead of $0. Which statement best describes a potential consequence of this choice of scale?
   Answer: The graph will make the profit growth appear more dramatic than it actually is. Using a truncated axis (one that doesn't start at zero) can be misleading. By showing only the top portion of the values, the visual distance between the points is exaggerated relative to their actual values. This makes the increases seem much larger and more significant than they would on a graph starting at zero.
10. A scatterplot is created to show the relationship between the number of hours a student spends playing video games per week and their grade point average (GPA). The data points on the plot generally trend from the upper-left corner to the lower-right corner. Which of the following is a reasonable conclusion based on this description?
    Answer: An increase in hours spent playing video games tends to be associated with a decrease in GPA. A trend from the upper-left to the lower-right indicates a negative correlation: as one variable (hours playing video games) increases, the other variable (GPA) tends to decrease. Choice C is incorrect because correlation does not imply causation.
11. A stacked bar chart shows a company's revenue sources. In 2022, total revenue was $200,000, of which $50,000 came from services. In 2023, total revenue was $300,000, of which $120,000 came from services. By how many percentage points did the proportion of revenue from services increase from 2022 to 2023?
    Answer: 15 percentage points First, calculate the proportion of revenue from services for each year. In 2022: $50,000 / $200,000 = 0.25, or 25%. In 2023: $120,000 / $300,000 = 0.40, or 40%. The increase in percentage points is the difference between these two percentages: 40% - 25% = 15 percentage points.
12. A family's $5,000 monthly budget is represented by a circle graph. Housing accounts for 30%, Food for 20%, Transportation for 15%, Savings for 10%, and 'Other' for the remainder. How much more money is allocated to Housing and Food combined than to Savings and Transportation combined?
    Answer: $1,250 First, calculate the total percentage for each category combination. Housing and Food: 30% + 20% = 50%. Savings and Transportation: 10% + 15% = 25%. Next, find the difference in percentages: 50% - 25% = 25%. Finally, calculate the dollar amount of this difference: 25% of $5,000 is 0.25 * 5000 = $1,250.
13. A report compares test scores for two classes using box plots. The box plot for Class A shows a median score of 80 and an interquartile range (IQR) of 15. The box plot for Class B also shows a median score of 80, but an IQR of 25. Based on this information, what can be concluded?
    Answer: The middle 50% of scores in Class A are less spread out than in Class B. The interquartile range (IQR) represents the spread of the middle 50% of the data. Since Class A has a smaller IQR (15) than Class B (25), the scores of the middle 50% of students in Class A are closer together, or less spread out. The medians are equal, so we cannot conclude one class performed better. The IQR does not determine the overall range or the mean.
14. A table shows the number of subscribers to a service at the end of each year: Year 1: 1.2 million; Year 2: 1.5 million; Year 3: 2.1 million; Year 4: 3.0 million. In the interval between which two consecutive years was the percent growth in subscribers the greatest?
    Answer: Between Year 3 and Year 4 Calculate the percent growth for each interval: (New-Old)/Old. Year 1 to 2: (1.5-1.2)/1.2 = 0.3/1.2 = 25%. Year 2 to 3: (2.1-1.5)/1.5 = 0.6/1.5 = 40%. Year 3 to 4: (3.0-2.1)/2.1 = 0.9/2.1 ≈ 42.9%. The greatest percentage growth occurred between Year 3 and Year 4.
15. The double bar graph compares the number of books read by students in Class A and Class B over four months. Based on the graph shown, what is the difference between the mean monthly number of books read by Class A and the mean monthly number of books read by Class B?
    Answer: 2.5 books Class A totals: 12 + 15 + 18 + 23 = 68; mean = 68/4 = 17. Class B totals: 10 + 14 + 16 + 18 = 58; mean = 58/4 = 14.5. Difference = 17 − 14.5 = 2.5. (A) 1.5 comes from using the median difference. (B) 2.0 comes from an arithmetic error averaging only three months. (D) 6.0 is the difference for the final month only (23−18=5 or related misread), not the mean difference.
16. The line graph shows the population (in thousands) of a town from 2010 to 2020. Based on the graph shown, during which two-year period did the population experience the greatest percent increase?
    Answer: 2012 to 2014 Percent increases: 2010–2012: (24−20)/20 = 4/20 = 20%; 2012–2014: (30−24)/24 = 6/24 = 25%; 2014–2016: (33−30)/30 = 3/30 = 10%; 2018–2020: (42−36)/36 = 6/36 ≈ 16.7%. The 2012–2014 period had the greatest percent increase at 25%. (A) 20% is the second largest. (C) 10% is the smallest. (D) ≈16.7% is third largest. Students who compare raw differences might be misled since both 2012–14 and 2018–20 had increases of 6 thousand, but percent increase accounts for the different starting values.
17. Use the table above to answer the question. The table shows total sales (in thousands of dollars) for four regions across two years. Which region had the greatest percent increase in sales from 2022 to 2023?
    Answer: West Percent increases: North = (180−150)/150 = 20%; South = (225−200)/200 = 12.5%; East = (120−90)/90 ≈ 33.3%; West = (84−60)/60 = 40%. West has the greatest percent increase. (A) is the largest raw increase among three regions but not percent. (B) has the largest sales total but smallest percent increase. (C) is a strong distractor at 33.3%, chosen by students who stop at East without checking West.
18. The scatterplot shows the relationship between hours studied (x) and test score (y) for 12 students, along with the line of best fit. Based on the scatterplot shown, approximately what test score does the line of best fit predict for a student who studies for 6.5 hours?
    Answer: 86 The line of best fit passes through approximately (2, 65) and (8, 92). Slope ≈ (92−65)/(8−2) = 27/6 = 4.5. Using point-slope: y = 65 + 4.5(x−2). At x = 6.5: y = 65 + 4.5(4.5) = 65 + 20.25 ≈ 85.25, which rounds to 86. (A) 74 results from reading the lowest cluster of actual points rather than the line. (B) 82 results from using a slope of about 3.4 (misreading the line's endpoints). (D) 92 is the y-value at x = 8, not x = 6.5.
19. A pie chart shows the distribution of a company's 50 employees across four departments: Sales (40%), Marketing (30%), Tech (20%), and Admin (10%). Based on this chart, which of the following statements is a valid conclusion?
    Answer: The Sales department has exactly 20 employees. A pie chart shows proportions at a single point in time. We can only make direct calculations based on the data given. The number of employees in Sales is 40% of 50, which is 0.40 * 50 = 20. The other statements infer value (importance), other data (salary), or future trends, none of which can be concluded from the chart.
20. A survey of 100 adults asked about home and car ownership. The results showed that 60 adults own a car, 50 adults own a home, and 20 adults own neither a car nor a home. According to this data, how many of the surveyed adults own both a car and a home?
    Answer: 30 Use the principle of inclusion-exclusion: Total = (Group A) + (Group B) - (Both) + (Neither). Here, 100 = 60 (Car) + 50 (Home) - (Both) + 20 (Neither). Simplifying gives 100 = 130 - (Both). Solving for (Both), we find that 30 adults own both a car and a home.

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