Question

the histogram shows the distribution of the number of representatives in the u.s. house of representatives for the 50 states. the four largest values (26, 28, 38, and 52) are all outliers. which of the following boxplots could also represent the distribution of the number of representatives in the u.s. house of representatives? a) box - plot a b) box - plot b c) box - plot c d) box - plot d e) box - plot e

Explanation:

Step1: Analyze key - features of boxplot

In a boxplot, outliers are represented as individual points outside the whiskers. The four largest values (26, 28, 38, and 52) are outliers. The box in the box - plot represents the inter - quartile range (IQR), with the line inside the box representing the median. The whiskers extend to the non - outlier minimum and maximum values.

Step2: Check each option

Option A: The whisker extends too far to represent the given outliers situation.
Option B: The box is positioned in a way that does not match the distribution shown in the histogram.
Option C: This boxplot has a box and whisker configuration that does not match the data distribution and outlier situation.
Option D: The boxplot has a correct representation of the box (IQR) and the outliers are placed correctly outside the whiskers, which aligns with the histogram data.
Option E: The whisker and box configuration does not match the data and outlier information from the histogram.

Answer:

D.