Use the image to answer the question.

Question

An illustration shows two sets of dot plots. One is titled City A Daily High Temperature in degrees Fahrenheit, and the other is City B Daily High Temperature in degrees Fahrenheit. The plots are shown as an abacus-like representation with dots in a vertical row over each number on a number line. For City A, a number line with arrows on both ends ranges from 68 to 74 in increments of 1. There are 2 dots above 68, 1 dot above 69, 2 dots above 70, 3 dots above 71, 2 dots above 72, 2 dots above 73, and one dot above 74. For City B, a number line with arrows on both ends ranges from 79 to 85 in increments of 1. There is 1 dot above 79, 2 dots above 80, 2 dots above 81, 3 dots above 82, 2 dots above 83, 2 dots above 84, and 1 dot above 85.

The dot plots show the daily high temperatures in two cities on 13 randomly chosen days in August. Which of the following informal assessments is true about these two distributions?

(1 point)
Responses

These distributions have significantly different variability.
These distributions have significantly different variability.

Data values in both distributions have similar spread.
Data values in both distributions have similar spread.

Based on visual overlap of the distribution, all data values overlap.
Based on visual overlap of the distribution, all data values overlap.

Both distributions have outliers.

Answer 1

Based on the given descriptions of the dot plots for City A and City B, we can analyze the informal assessments provided:

1. These distributions have significantly different variability. - This statement is accurate because the range of temperatures is much narrower for City A (68 to 74) compared to City B (79 to 85). The variability in City B is higher due to a wider spread.

2. Data values in both distributions have similar spread. - This statement is not true as the temperature ranges are different, indicating different spreads.

3. Based on visual overlap of the distribution, all data values overlap. - This statement is incorrect. There is no overlap in temperature values; City A's temperatures are entirely below City B's.

4. Both distributions have outliers. - This assessment could be subjective but given the data described, there do not appear to be any extreme values that can be categorized as outliers in either city.

Given this analysis, the correct response is: These distributions have significantly different variability.