Foundations: Descriptive Stats and Basics

  1. A dataset has values: 3, 3, 4, 6, 9. What is the median? A) 3 B) 4 C) 5 D) 6 Answer: B Explanation: Sorted data has middle value 4.

  2. The mode of 2, 4, 4, 5, 6 is: A) 2 B) 4 C) 5 D) 6 Answer: B Explanation: 4 occurs most often.

  3. Which measure is most affected by an extreme outlier? A) Mean B) Median C) Mode D) IQR Answer: A Explanation: Mean is sensitive to extreme values; median and IQR are robust.

  4. The range of 10, 12, 15, 20 is: A) 5 B) 8 C) 10 D) 12 Answer: C Explanation: Max − Min = 20 − 10 = 10.

  5. If you add the same constant k to every data point, the standard deviation: A) Increases by k B) Decreases by k C) Is unchanged D) Doubles Answer: C Explanation: SD measures spread; shifting doesn’t change spread.

  6. For a perfectly symmetric distribution, which is true? A) Mean < Median B) Mean = Median C) Mean > Median D) No relation Answer: B Explanation: Symmetry centers mean and median at the same point.

  7. The 75th percentile is the: A) First quartile B) Second quartile C) Third quartile D) IQR Answer: C Explanation: Q3 is the 75th percentile.

  8. The IQR is: A) Q3 − Q1 B) Q2 − Q1 C) Max − Min D) Mean − Median Answer: A Explanation: Interquartile range spans the middle 50%.

  9. A histogram with a long right tail is: A) Left-skewed B) Right-skewed C) Symmetric D) Uniform Answer: B Explanation: Long right tail = positive skew.

  10. The variance is measured in: A) Same units as data B) Square of units C) No units D) Reciprocal units Answer: B Explanation: Variance squares deviations.

  11. A boxplot displays all except: A) Median B) Quartiles C) Mean D) Outliers (as points) Answer: C Explanation: Standard boxplots don’t include the mean.

  12. Z-score tells: A) Rank B) Percentile exactly C) Distance from mean in SD units D) Distance from median Answer: C Explanation: z = (x − mean)/SD.

  13. If mean = 50 and SD = 10, a value of 70 has z-score: A) 1 B) 1.5 C) 2 D) −2 Answer: C Explanation: (70 − 50)/10 = 2.

  14. A discrete variable example: A) Height B) Time C) Number of calls D) Temperature Answer: C Explanation: Counts take integer values.

  15. Standardizing data (z-scores) changes: A) Shape only B) Center and spread, not shape C) Shape and spread D) Shape and center Answer: B Explanation: Linear transform to mean 0, SD 1; shape preserved.