Quantitative Literacy Data Interpretation Flashcards

A researcher reports that the median household income in City A is R28 500 and the mean is R41 200. Which conclusion is best supported by this information?

Answer: The income distribution is positively skewed, with a minority of high earners pulling the mean upward.

When the mean exceeds the median, the distribution is positively (right) skewed. A small number of very high incomes inflate the mean while the median—resistant to outliers—stays lower, indicating most households earn less than the mean.

A pie chart shows that Category X occupies a sector of 108°. If the total value represented by the chart is 6 000 units, what is the value represented by Category X, and what percentage of the total does it represent?

Answer: 1 800 units; 30%

A full circle is 360°. The fraction for Category X is 108/360 = 0.30, or 30%. Multiplying 6 000 × 0.30 gives 1 800 units. Always convert the sector angle to a fraction of 360° before calculating the value or percentage.

The table below shows quarterly sales (in thousands of rands) for a company over two years: Q1 Y1: 120 | Q2 Y1: 145 | Q3 Y1: 98 | Q4 Y1: 167 Q1 Y2: 131 | Q2 Y2: 159 | Q3 Y2: 87 | Q4 Y2: 182 A manager claims sales grew by approximately 8% year-on-year. Which calculation best evaluates this claim?

Answer: Sum Y1 totals (530) and Y2 totals (559), then compute (559−530)/530 × 100 ≈ 5.5% — the claim overstates growth.

Year-on-year revenue growth should compare total annual revenue. Y1 total = 120+145+98+167 = 530; Y2 total = 131+159+87+182 = 559. Growth = (559−530)/530 × 100 ≈ 5.5%, not 8%. Comparing only one quarter or averaging percentage changes are methodologically flawed approaches.

A scatter plot of study hours (x-axis) vs. test scores (y-axis) for 60 students shows a strong positive linear correlation (r = 0.87). A student who studied 0 hours is predicted by the regression line to score 34 points. What is the most accurate interpretation of this intercept value?

Answer: The model predicts a baseline score of 34 for zero study hours, but this may not be meaningful if no students actually studied 0 hours.

A regression intercept represents the predicted y-value when x = 0. However, if x = 0 lies outside the range of observed data (extrapolation), the prediction may not be meaningful in context. The intercept is a mathematical artifact of fitting the line, not necessarily a guaranteed real-world outcome. Correlation also does not imply causation.

An index measuring cost of living uses 2018 as the base year (index = 100). By 2022, the index stood at 134. By 2024, the index stood at 148. What was the percentage increase in the cost of living from 2022 to 2024 only?

Answer: 10.4%

To find the change from 2022 to 2024, use the 2022 index as the new base: (148 − 134) / 134 × 100 ≈ 10.4%. The 48% figure measures growth from the original 2018 base, not from 2022. A common error is subtracting index numbers directly (148 − 134 = 14) and treating 14 as a percentage, which is incorrect.

A double bar chart compares male and female unemployment rates across five provinces. Province C shows males at 18% and females at 27%. The province's overall working-age population is 2 400 000, split 52% female and 48% male. Approximately how many people in Province C are unemployed?

Answer: 554 400

Male working-age population: 2 400 000 × 0.48 = 1 152 000. Unemployed males: 1 152 000 × 0.18 = 207 360. Female working-age population: 2 400 000 × 0.52 = 1 248 000. Unemployed females: 1 248 000 × 0.27 = 336 960. Total unemployed: 207 360 + 336 960 = 544 320 ≈ 554 400 (nearest answer). This tests whether students apply gender-specific rates to gender-specific sub-populations rather than averaging the rates and applying to the whole.