The ordered data set $\{4, 9, 14, 18, 23\}$ has a range of $19$ and an IQR of $14$. Which measure better represents the spread if an outlier of $100$ is added?

Range, because it uses all values

IQR, because it is not affected by the outlier

Both measures are equally reliable

Neither measure describes spread

Team X has an IQR of $5$ points per game. Team Y has an IQR of $18$ points per game. Which team is more consistent, and why?

Team Y, because a larger IQR means more scoring

Team X, because a smaller IQR means the middle 50% of scores are tightly clustered

Team X, because it has a smaller range

Team Y, because a larger IQR means less variability

11-2 Measures of Spread Practice — Grade 9 math

11-2 Measures of Spread — Practice Questions

1. Given the ordered data set $\{2, 4, 7, 11, 13, 15\}$, the median is ___.
2. For the ordered data set $\{3, 6, 8, 12, 15, 17, 20\}$, the IQR equals ___.
3. The ordered data set $\{4, 9, 14, 18, 23\}$ has a range of $19$ and an IQR of $14$. Which measure better represents the spread if an outlier of $100$ is added?
- A. Range, because it uses all values
- B. IQR, because it is not affected by the outlier
- C. Both measures are equally reliable
- D. Neither measure describes spread
4. For the ordered data set $\{5, 10, 10, 14, 18, 22, 25, 30\}$, the five-number summary is $(5, \_, 16, \_, 30)$. What is $Q_1$?
5. Team X has an IQR of $5$ points per game. Team Y has an IQR of $18$ points per game. Which team is more consistent, and why?
- A. Team Y, because a larger IQR means more scoring
- B. Team X, because a smaller IQR means the middle 50% of scores are tightly clustered
- C. Team X, because it has a smaller range
- D. Team Y, because a larger IQR means less variability
6. For the dataset $\{5, 7, 9, 11, 8\}$, the mean is $\bar{x} = 8$. The sum of squared deviations is ___.
7. For the dataset $\{5, 7, 9, 11, 8\}$ with $n = 5$ and sum of squared deviations $= 20$, the sample variance is ___.
8. A dataset has a sample variance of $s^2 = 36$. What is the sample standard deviation $s$?
- A. $s = 6$
- B. $s = 18$
- C. $s = 12$
- D. $s = 1296$
9. Two teams both have a mean of 74 points. Team A has $s = 3$ and Team B has $s = 15$. Which statement best describes the data?
- A. Team A's scores are more spread out than Team B's
- B. Team B's scores are more spread out than Team A's
- C. Both teams have the same spread
- D. Team A has a higher mean than Team B
10. Which of the following datasets has a standard deviation of $s = 0$?
- A. $\{4, 4, 4, 4\}$
- B. $\{1, 2, 3, 4\}$
- C. $\{0, 4, 8, 12\}$
- D. $\{3, 4, 5, 6\}$