NBT Quantitative Literacy: Charts, Tables and Graphs Flashcards

A double bar chart shows monthly sales for two products over 6 months. Product A's bars are consistently taller than Product B's, yet the chart's legend is accidentally swapped. If the chart shows Product A's total as 4 200 units and Product B's total as 2 800 units, but the legend is reversed, what is the actual ratio of the higher-selling product's total to the lower-selling product's total?

Answer: 3:2

Because the legend is swapped, the bars labelled 'Product B' actually belong to the higher-selling product (4 200 units) and vice versa. The true ratio of the higher-selling product to the lower-selling product is 4 200 : 2 800, which simplifies to 3 : 2.

A cumulative frequency table lists test scores in intervals. The cumulative frequency up to 50 is 12, up to 60 is 30, up to 70 is 54, up to 80 is 72, and up to 90 is 80 (the total). A student claims the modal class is 60–70 because it has the highest cumulative frequency jump. A second student says it is 70–80. Which student is correct, and what is the frequency of the modal class?

Answer: First student; frequency = 24

The frequency of each class is found by subtracting successive cumulative frequencies: 50–60 gives 18, 60–70 gives 24, 70–80 gives 18, 80–90 gives 8. The largest single-class frequency is 24 (the 60–70 interval), so the first student is correct and the modal class frequency is 24.

A pie chart represents a company's expenditure. The sector for salaries subtends an angle of 126°. If the total annual expenditure is R4 800 000 and salaries increased by 15% the following year while all other costs remained unchanged, what angle would the salary sector subtend in the new pie chart?

Answer: Approximately 138°

Current salary expenditure = (126/360) × 4 800 000 = R1 680 000. After a 15% increase, salaries = 1 680 000 × 1.15 = R1 932 000. The remaining expenditure is unchanged at R3 120 000, so the new total = R5 052 000. The new salary angle = (1 932 000 / 5 052 000) × 360 ≈ 137.7°, which rounds to approximately 138°.

A scatter plot of study hours (x-axis) vs. exam scores (y-axis) for 60 students shows a strong positive correlation. The line of best fit passes through the points (2, 45) and (8, 75). A student studied for 11 hours. Using the line of best fit, what score would be predicted, and why should this prediction be treated with caution?

Answer: Score of 90; caution because 11 hours is outside the data range (extrapolation)

Gradient = (75 − 45) / (8 − 2) = 5. Using point (2, 45): y = 5x + 35. At x = 11: y = 55 + 35 = 90. The caution is that 11 hours lies beyond the observed data range (extrapolation), making the prediction unreliable — the linear relationship may not hold outside the range of the data.

Two line graphs track the exchange rate of the rand against the dollar over 12 months. Graph A uses a vertical axis starting at R14.00 and ending at R16.00. Graph B shows the same data but with a vertical axis from R0 to R20.00. A journalist uses Graph A to argue the rand 'collapsed dramatically.' Which statement best evaluates this claim?

Answer: The claim is misleading because Graph A's truncated axis exaggerates the visual magnitude of the change

Graph A's y-axis starts at R14.00 rather than zero, compressing the visual scale so that a modest absolute change appears dramatic. Both graphs contain identical data, but Graph A's truncated axis misleads viewers into perceiving a larger relative collapse than actually occurred. This is a classic example of a misleading graph through axis manipulation.

A two-way table records 200 survey responses by gender and transport preference (car, taxi, bus). Males: car = 48, taxi = 22, bus = 10. Females: car = 36, taxi = 40, bus = 44. What is the probability that a randomly selected respondent who prefers taxi is female, expressed as a simplified fraction?

Answer: 20/31

Total taxi users = 22 (male) + 40 (female) = 62. Female taxi users = 40. P(female | taxi) = 40/62 = 20/31. This is a conditional probability — only those who prefer taxi form the sample space, not all 200 respondents.