Question

shapes of discrete distributions
histogram a
histogram b
histogram c
(a) which histogram is best described as unimodal?
histogram a histogram b histogram c
(b) which histogram is skewed to the right the most?
histogram a histogram b histogram c
(c) which histogram is the closest to being uniform?
histogram a histogram b histogram c
(d) which histogram is the closest to being symmetric?
histogram a histogram b histogram c

Explanation:

(a) Unimodal Histogram

Step1: Recall unimodal definition

A unimodal distribution has one peak. Histogram B has one distinct peak (at \(x = 20 - 22\)), while Histogram A has multiple peaks (more than one high - point) and Histogram C has a more irregular shape.

(b) Right - skewed Histogram

Step1: Recall right - skewed definition

A right - skewed distribution has a longer tail on the right. Histogram C has a longer tail on the right side (towards higher \(x\) values: \(18 - 24\)), while Histogram A is more irregular and Histogram B is more symmetric around its peak.

(c) Uniform Histogram

Step1: Recall uniform definition

A uniform distribution has bars of approximately equal height. Histogram A has bars that are more evenly distributed in height compared to Histogram B (which has a peak) and Histogram C (which has a tail).

(d) Symmetric Histogram

Step1: Recall symmetric definition

A symmetric distribution has a mirror - like shape around its center. Histogram B is more symmetric around its central peak (\(x = 20 - 22\)) compared to Histogram A (irregular) and Histogram C (right - skewed).

Answer:

(a) Histogram B
(b) Histogram C
(c) Histogram A
(d) Histogram B