Question

unit 4 test: graphs and describing distributions mul

1. the mean and median of a distribution are measures of

(a) the number of observations
(b) association
(c) variability or spread
(d) center
o a
o b
o c
o d

Explanation:

The mean is calculated as $\frac{\sum_{i = 1}^{n}x_{i}}{n}$ (sum of all data points divided by the number of data points), and the median is the middle - value when the data is ordered. Both of these measures aim to locate the central or typical value within a data distribution.

• Option (a): The number of observations is just a count ($n$ in the mean formula), and neither the mean nor the median directly represents this count.
• Option (b): Association is typically measured by correlation coefficients (e.g., Pearson's correlation coefficient) for two - variable relationships, not by the mean or median.
• Option (c): Variability or spread is measured by statistics like the range, variance ($\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}$ for sample variance), and standard deviation ($\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$ for sample standard deviation), not by the mean or median.
• Option (d): Since the mean and median both try to find the central tendency of a distribution, they are measures of the center.

Answer:

D. center