One-Variable Data: Distributions and Measures of Center and Spread Flashcards

A dataset of 9 numbers has a mean of 22. The sum of 8 of the numbers is 180. What is the 9th number?

Answer: 18

Total sum = 22 × 9 = 198; 9th number = 198 − 180 = 18.

Which measure of spread is most affected by a single extreme outlier?

Answer: Range

The range uses only the maximum and minimum values, so a single extreme outlier directly changes the range more dramatically than the IQR or standard deviation.

The scores 50, 60, 70, 80, and 90 form a dataset. A new value of 70 is added. Which statement about the updated dataset is true?

Answer: The mode changes from undefined to 70.

Originally all values are distinct, so there is no mode; adding a second 70 creates a mode of 70 while the mean stays at 70 and the median remains 70.

A histogram shows the following distribution of ages in a group: most values cluster between 20 and 30, with a few values near 70. This distribution is best described as:

Answer: Right-skewed

The bulk of data is on the lower end with a few high values creating a tail to the right, which is the definition of a right-skewed (positively skewed) distribution.

The IQR of a dataset is 18. Using the 1.5 × IQR rule, an outlier is any value more than 1.5 × IQR above Q3. If Q3 = 54, what is the outlier threshold?

Answer: 81

Upper outlier threshold = Q3 + 1.5 × IQR = 54 + 1.5 × 18 = 54 + 27 = 81.

Two datasets have the same mean of 50 but different standard deviations: Dataset A has σ = 2 and Dataset B has σ = 12. Which statement is true?

Answer: Dataset B is more spread out than Dataset A.

A larger standard deviation indicates greater spread around the mean; Dataset B (σ = 12) is far more spread out than Dataset A (σ = 2).

A dataset is: 2, 4, 4, 6, 8, 10. What is the difference between the mean and the median?

Answer: 1

Mean = (2+4+4+6+8+10)/6 = 34/6 ≈ 5.67; Median = (4+6)/2 = 5; difference ≈ 0.67, closest to 1.