NBT Data Interpretation & Analysis 3

Question 1

A box-and-whisker plot shows: minimum = 20, Q1 = 35, median = 50, Q3 = 65, maximum = 80. What is the interquartile range (IQR)?

Accepted Answer

30

Answer

IQR = Q3 - Q1 = 65 - 35 = 30.

Question 2

A frequency distribution shows: scores 0–49 (15 students), 50–74 (45 students), 75–100 (40 students). What percentage of students scored below 50?

Accepted Answer

15%

Answer

Total: 15 + 45 + 40 = 100 students. Percentage below 50: 15 ÷ 100 = 15%.

Question 3

Two datasets have the same mean but different standard deviations (SD₁ = 2, SD₂ = 10). What can be concluded?

Accepted Answer

Dataset 2 has more spread around the mean

Answer

Standard deviation measures the spread of data around the mean. Dataset 2 (SD = 10) has much more variability — its values are more spread out from the mean than Dataset 1 (SD = 2).

Question 4

A regression line on a scatter plot has the equation y = 3x + 5. What does the slope (3) tell us?

Accepted Answer

For every 1-unit increase in x, y increases by 3

Answer

The slope of a linear equation represents the rate of change. A slope of 3 means that for every 1-unit increase in x, the predicted value of y increases by 3.

Question 5

A researcher claims that because crime rates and ice cream sales both rise in summer, ice cream causes crime. What is wrong with this reasoning?

Accepted Answer

Correlation does not imply causation — both are affected by a third variable (heat/summer)

Answer

This is a classic confounding variable (lurking variable) example. Both variables are influenced by a third factor (hot weather/summer) — not by each other. Correlation ≠ causation.

(NBT) National Benchmark Test Practice Test

(NBT) National Benchmark Test Practice Test

NBT Data Interpretation & Analysis 3