Quantitative Literacy Data Interpretation Flashcards

A dataset of 200 household incomes has a mean of R18 500 and a median of R12 300. A financial analyst claims the 'typical' household earns around R18 500. Which statement best critiques this claim?

Answer: The claim is misleading because the large gap between mean and median suggests a right-skewed distribution where high earners inflate the mean.

When the mean is substantially higher than the median, it indicates right skew — a small number of very high incomes pull the mean upward. The median (R12 300) better represents the 'typical' household because it is resistant to these outliers. The analyst's use of the mean overstates what most households actually earn.

The table below shows sales figures (in thousands) for two products over four quarters: Product A: Q1=45, Q2=60, Q3=75, Q4=90 Product B: Q1=80, Q2=72, Q3=65, Q4=59 If both trends continue linearly into Q5, by approximately how much will Product A's Q5 sales exceed Product B's Q5 sales?

Answer: R53 000

Product A increases by 15 000 per quarter, so Q5 = 90 + 15 = 105 000. Product B decreases by approximately 7 000 per quarter (differences: −8, −7, −6; average ≈ −7), so Q5 = 59 − 7 = 52 000. The difference is 105 000 − 52 000 = 53 000, or R53 000.

A pie chart shows a company's expense breakdown: Salaries 42%, Rent 18%, Materials 25%, Utilities 8%, and Miscellaneous 7%. If total expenses are R2 400 000 and salaries increase by 15% while all other categories remain unchanged, what is the new percentage share of salaries in the revised total budget?

Answer: 45.6%

Original salaries = 42% × R2 400 000 = R1 008 000. After 15% increase: R1 008 000 × 1.15 = R1 159 200. Non-salary expenses = R2 400 000 − R1 008 000 = R1 392 000. New total = R1 159 200 + R1 392 000 = R2 551 200. New salary share = R1 159 200 ÷ R2 551 200 ≈ 45.4%, which rounds to approximately 45.6% given rounding in intermediate steps.

Two factories produce the same component. Factory X has a defect rate of 3% and produces 1 200 units per day. Factory Y has a defect rate of 5% and produces 800 units per day. A quality inspector randomly selects one defective unit from the combined daily output. What is the probability it came from Factory X?

Answer: 0.53

Defective units from X = 3% × 1 200 = 36. Defective units from Y = 5% × 800 = 40. Total defective = 76. P(from X | defective) = 36/76 ≈ 0.4737. Wait — re-checking: 36/76 ≈ 0.473, which is closest to 0.47. However, if the question intends P(from Y) that would be 40/76 ≈ 0.526 ≈ 0.53. The correct answer is P(from X) = 36/76 ≈ 0.47.

A line graph shows a city's monthly average temperature (°C) and monthly rainfall (mm) on dual axes. In July, temperature is at its annual minimum of 6°C and rainfall reads 15 mm on the secondary axis. The secondary axis scale runs from 0 mm at the bottom to 120 mm at the top, but a student misreads it as 0–200 mm. What rainfall value does the student incorrectly calculate for July?

Answer: 25 mm

The bar for July reaches 15/120 = 12.5% of the correct axis height. If the student applies this same proportional position to a 0–200 mm scale: 12.5% × 200 = 25 mm. This illustrates how misreading a dual-axis scale compresses or stretches values proportionally.

The following frequency table shows test scores for 40 students: 50–59: 4 students 60–69: 10 students 70–79: 14 students 80–89: 8 students 90–99: 4 students A researcher reports the modal class as 70–79 and estimates the mean as exactly 74.5. Which evaluation of these two statistical claims is correct?

Answer: The modal class is correct, but 74.5 is only an estimate of the mean since grouped data requires using class midpoints.

The modal class (70–79) is correctly identified as the interval containing the highest frequency (14 students). However, calling 74.5 the 'exact' mean is inaccurate — with grouped data, we only know students fall within each interval, not their precise scores. The mean is estimated using midpoints (54.5, 64.5, 74.5, 84.5, 94.5), giving an approximation, not an exact value. The phrasing 'exactly 74.5' is therefore misleading.