Question

unit 4 test: graphs and describing distributions multiple choi

1. for a distribution that is skewed to the right, usually

(a) the mean will be larger than the median.
(b) the median will be larger than the mean.
(c) the first quartiles will be larger than the third quartile.
(d) the standard deviation will be negative.
(e) the minimum will be larger than the maximum.
○ a
○ b
○ c
○ d
○ e

Explanation:

In a right - skewed distribution, the tail is on the right side. The mean is pulled in the direction of the tail (right), while the median is less affected by extreme values. So, the mean is larger than the median.

• Option (b) is incorrect because it has the relationship between mean and median reversed.
• Option (c) is incorrect because in any distribution \(Q_1
• Option (d) is incorrect because the standard deviation \(\sigma=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\mu)^2}{n}}\) (for a population) or \(s=\sqrt{\frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n - 1}}\) (for a sample) is a non - negative quantity as it is a square root of a non - negative number.
• Option (e) is incorrect because by definition, the minimum \(x_{\min}\leq x_{\max}\) (minimum value is less than or equal to the maximum value) in a data set.

Answer:

A. the mean will be larger than the median.