Interpreting Data from Tables - ACT Science

1. Calculate the mean of these values: 10, 20, 30, 40.

   The mean is 25. Sum divided by count: $(10+20+30+40)/4 = 100/4 = 25$.

2. What is the maximum value in this dataset: 3, 7, 11, 6?

   The maximum value is 11. Compare all values to find the largest.

3. What is $y$ at $x=4$ if a table shows a linear pattern: $(1,3)$, $(2,5)$, $(3,7)$?

   $9$. Pattern increases by 2 each step: $7+2=9$.

4. What is the percent change from $80$ to $60$ for a table value that decreases?

   $-25\%$. $(60-80)/80 \times 100\% = -25\%$.

5. What does it mean if a column is labeled "Concentration (mg/L)"?

   Each value is a concentration measured in $\text{mg}/\text{L}$. Mass per volume unit indicates solution strength.

6. What is the mean of the table values $4, 6, 8$?

   $6$. Sum divided by count: $(4+6+8)/3=6$.

7. What is the correct first step when interpreting a scientific data table?

   Read the title and all headers (including units). Understanding structure prevents misinterpretation of data.

8. What is the difference between two table entries $18.6$ and $17.9$?

   $0.7$. Subtraction finds the absolute difference.

9. What is the correct interpretation if a table shows identical values for all trials under one condition?

   The measured outcome is constant across those trials. No variation suggests controlled or stable conditions.

10. A table column is "Time (min)" and another is "Distance (m)"; what are the units of $\frac{\Delta d}{\Delta t}$?

    $\text{m}/\text{min}$. Distance per time gives velocity units.

11. What does it mean if two columns increase together across rows in a table?

    They show a positive association in the listed range. Variables change in the same direction together.

12. If a table lists "Temperature (°C)" what is the temperature in °C for the entry labeled $25$?

    $25\,^{\circ}\text{C}$. The value directly gives degrees Celsius.

13. Which column shows consistent growth if values are 2, 4, 8?

    Exponential growth. Each value doubles: geometric growth pattern.

14. Convert the table value $450\,\text{mg}$ to grams using $1000\,\text{mg}=1\,\text{g}$.

    $0.45\,\text{g}$. Divide by conversion factor: $450/1000$.

15. Determine the smallest value in the dataset: 19, 7, 14, 22.

    The smallest value is 7. Compare all values to find the minimum.

16. Identify the median of the dataset: 8, 3, 5, 7, 10.

    The median is 7. Sort the data and find the middle value: 3, 5, 7, 8, 10.

17. Determine the smallest value in the dataset: 15, 12, 9, 18.

    The smallest value is 9. Compare all values to find the smallest.

18. Identify the correct rule for selecting a value when asked for the "closest" table value.

    Choose the entry with smallest absolute difference. Minimize distance to find the nearest match.

19. Identify the median of these values: 9, 2, 5, 7, 3.

    The median is 5. Sort and find middle: 2, 3, 5, 7, 9.

20. What does the unit shown in a table header indicate about every value in that column?

    Each entry is measured in that unit. The unit applies uniformly to all data in that column.

21. Find the interpolated value at $x=5$ if a table shows $(4, 20)$ and $(6, 30)$ with a linear trend.

    $25$. Linear interpolation: $20 + (30-20) \times (5-4)/(6-4)$.

22. Which value is the mode in this dataset: 2, 4, 4, 5, 6?

    The mode is 4. The value 4 appears twice, more than others.

23. What is the range of this dataset: 3, 8, 13, 18?

    The range is 15. Maximum minus minimum: $18 - 3 = 15$.

24. What is the meaning of "range" for a set of table values?

    Range $=$ maximum minus minimum. Measures the spread of data values.

25. What is the mode in this dataset: 4, 4, 6, 8, 9?

    The mode is 4. The value that appears most frequently in the dataset.

26. Identify the minimum in the table set $\{0.12, 0.08, 0.15, 0.10\}$.

    $0.08$. Smallest value in the given set.

27. What is the dependent variable in a table when one column is explicitly labeled as such?

    The column labeled dependent variable. The response variable is what experimenters measure.

28. Calculate the mean of the dataset: 12, 15, 11, 14.

    The mean is 13. Sum all values and divide by count: $(12+15+11+14)/4 = 52/4 = 13$.

29. What is the independent variable in a table when one column is explicitly labeled as such?

    The column labeled independent variable. The manipulated variable is what experimenters control.

30. What is the range of this dataset: 5, 10, 15, 20?

    The range is 15. Maximum minus minimum: $20 - 5 = 15$.

31. What is the slope between table points $(t, y)$ of $(2, 5)$ and $(6, 13)$?

    $2$. Rise over run: $(13-5)/(6-2)=2$.

32. What does it mean if one column increases while another decreases across rows in a table?

    They show a negative association in the listed range. Variables change in opposite directions.

33. What is the sum of all values in the dataset: 1, 2, 3, 4?

    The sum is 10. Add all values together: $1 + 2 + 3 + 4 = 10$.

34. What does a table entry written as "$3.2\pm 0.1$" typically represent?

    A value with uncertainty: $3.2$ with margin $0.1$. Plus-minus notation shows measurement uncertainty.

35. Convert the table value $2.5\,\text{L}$ to milliliters using $1\,\text{L}=1000\,\text{mL}$.

    $2500\,\text{mL}$. Multiply by conversion factor: $2.5 \times 1000$.

36. Find the sum of the dataset: 11, 13, 15, 17.

    The sum is 56. Add all values: $11 + 13 + 15 + 17 = 56$.

37. Determine the smallest value in the dataset: 8, 5, 12, 15.

    The smallest value is 5. Compare all values to find the smallest.

38. Which value is the mode in this dataset: 9, 3, 9, 6, 7?

    The mode is 9. The value 9 appears twice, more than others.

39. What does the symbol "$\times 10^n$" in a table header tell you to do to each listed value?

    Multiply each listed value by $10^n$. Scientific notation scaling factor for large/small values.

40. What is the range of this dataset: 4, 9, 15, 20?

    The range is 16. Maximum minus minimum: $20 - 4 = 16$.

41. What is the range of this dataset: 10, 15, 20, 25?

    The range is 15. Maximum minus minimum: $25 - 10 = 15$.

42. Calculate the mean of the dataset: 6, 8, 10, 12.

    The mean is 9. Sum divided by count: $(6+8+10+12)/4 = 36/4 = 9$.

43. What is the range of the table values $3, 7, 7, 10$?

    $7$. Maximum minus minimum: $10-3=7$.

44. What is the correct action if a question asks for a value "between" two table entries not explicitly listed?

    Estimate by interpolation between the nearest entries. Use proportional reasoning between known points.

45. Identify the median of these values: 5, 13, 8, 10, 12.

    The median is 10. Sort and find middle: 5, 8, 10, 12, 13.

46. What is the correct conclusion if a table shows overlapping uncertainty ranges for two conditions?

    A clear difference is not established by the data alone. Uncertainty overlap prevents definitive comparison.

47. What is the ratio of two table values $12$ and $3$, expressed as $\frac{12}{3}$?

    $4$. Division gives the multiplicative relationship.

48. What is the maximum value in this dataset: 4, 10, 9, 3?

    The maximum value is 10. Compare all values to find the largest.

49. Which value is the mode in this dataset: 1, 2, 2, 3, 4?

    The mode is 2. The value 2 appears twice, more than others.

50. Identify the median of the dataset: 14, 7, 12, 9, 11.

    The median is 11. Sort and find middle: 7, 9, 11, 12, 14.

51. Calculate the mean of the dataset: 20, 25, 30, 35.

    The mean is 27.5. Sum divided by count: $(20+25+30+35)/4 = 110/4 = 27.5$.

52. Which value is larger: $0.08$ or $7\times 10^{-2}$ (as might appear in a table)?

    $0.08$. $7 \times 10^{-2} = 0.07 < 0.08$.

53. Find the sum of this dataset: 3, 5, 7, 9.

    The sum is 24. Add all values: $3 + 5 + 7 + 9 = 24$.

54. What is the correct way to compare two conditions in a table when the units differ?

    Convert to consistent units before comparing. Unit consistency is required for valid comparisons.

55. Calculate the mean of the dataset: 5, 10, 15, 20.

    The mean is 12.5. Sum divided by count: $(5+10+15+20)/4 = 50/4 = 12.5$.

56. Find the sum of this dataset: 7, 9, 11, 13.

    The sum is 40. Add all values: $7 + 9 + 11 + 13 = 40$.

57. Identify the median of these values: 6, 3, 8, 5, 9.

    The median is 6. Sort and find middle: 3, 5, 6, 8, 9.

58. Identify the median of the dataset: 5, 3, 8, 9, 2.

    The median is 5. Sort data and find the middle: 2, 3, 5, 8, 9.

59. What is the maximum value in this dataset: 2, 4, 6, 8?

    The maximum value is 8. Compare all values to identify the largest.

60. What is the percent change from $50$ to $65$ for a table value that increases?

    $30\%$. $(65-50)/50 \times 100\% = 30\%$.

61. Find the sum of the dataset: 4, 6, 8, 10.

    The sum is 28. Add all values: $4 + 6 + 8 + 10 = 28$.

62. What is the range of the dataset: 2, 5, 9, 12?

    The range is 10. Subtract minimum from maximum: $12 - 2 = 10$.

63. What is the mean value of data points 3, 5, 7, and 9?

    The mean is 6. Sum all values and divide by the count: $(3+5+7+9)/4 = 24/4 = 6$.

64. What is the correct interpretation if a table shows a monotonic decrease down a column as the independent variable increases?

    The dependent variable decreases as the independent variable increases. Inverse relationship between variables is evident.

65. What is the maximum value in this dataset: 1, 4, 7, 3?

    The maximum value is 7. Compare all values to identify the largest.

66. Which table value is closest to $5.0$: $4.7$, $5.4$, or $5.2$?

    $5.2$. Distance from $5.0$: $0.3$, $0.4$, $0.2$ respectively.

67. Determine the smallest value in this dataset: 9, 8, 7, 5.

    The smallest value is 5. Compare all values to identify the minimum.

68. Which value is the mode of the dataset: 7, 8, 7, 5, 9?

    The mode is 7. The value 7 appears twice, more than any other value.

69. What is the meaning of "mean" in a table summary row labeled "Mean"?

    Average value: sum divided by number of entries. Standard statistical measure of central tendency.

70. What does a footnote marker (such as "*") next to a table value indicate?

    A special condition or note applies to that value. Footnotes provide additional context or exceptions.

71. What is the average of two replicate table measurements $10.2$ and $10.6$?

    $10.4$. Sum divided by two: $(10.2+10.6)/2$.

72. What is the median of the ordered values $2, 5, 9, 12, 20$ in a table row?

    $9$. Middle value when data is arranged in order.

73. What does a blank cell in a data table most commonly represent in ACT Science contexts?

    No data recorded or not applicable for that condition. Missing data indicates measurement wasn't taken.

74. What is the meaning of "percent change" from an initial to a final table value?

    $\frac{\text{final}-\text{initial}}{\text{initial}}\times 100\%$. Standard formula for relative change calculation.

75. Find the sum of the dataset: 6, 2, 4, 8.

    The sum is 20. Add all values: $6 + 2 + 4 + 8 = 20$.

76. Which value is the mode in this dataset: 3, 5, 5, 7, 8?

    The mode is 5. The value 5 appears twice, more than others.

77. If Column B has values 3, 4, 5, what is the percentage increase from 3 to 5?

    66.67%. Change from 3 to 5 is 2/3 = 66.67%.

78. Which value represents the range of 3, 8, 2, 10?

    The range is 8. Subtract the smallest from the largest: $10 - 2 = 8$.

79. Determine the smallest value in the dataset: 6, 9, 3, 5.

    The smallest value is 3. Compare all values to find the minimum.

80. What is the correct interpretation if a table shows a monotonic increase down a column as the independent variable increases?

    The dependent variable increases as the independent variable increases. Direct relationship between variables is evident.

81. What is the rate if a table shows mass increases from $10\,\text{g}$ to $16\,\text{g}$ in $3\,\text{s}$?

    $2\,\text{g}/\text{s}$. Change in mass over time: $(16-10)/3=2$.

82. Identify the maximum in the table set $\{2.1, 2.4, 1.9, 2.3\}$.

    $2.4$. Largest value in the given set.

83. What is the meaning of "rate" when computed from two table entries over time?

    Rate $=\frac{\Delta \text{quantity}}{\Delta \text{time}}$. Change per unit time measures process speed.

84. What is the maximum value in this dataset: 10, 25, 15, 5?

    The maximum value is 25. Compare all values to identify the largest.

Study these flashcards