Question

1. suspension bridges the lengths (in feet) of the main span of the longest suspension bridges in the united states and the rest of the world are shown below. which set of data is more variable?

united states 4205, 4200, 3800, 3500, 3478, 2800, 2800, 2310 s = 1293.9
world 6570, 5538, 5328, 4888, 4626, 4544, 4518, 3970 s = 803.2

1. hospital emergency waiting times the mean of the waiting times in an emergency room is 80.2 minutes with a standard deviation of 10.5 minutes for people who are admitted for additional treatment. the mean waiting time for patients who are discharged after receiving treatment is 120.6 minutes with a standard deviation of 18.3 minutes. which times are more variable?

Explanation:

Step1: Calculate the coefficient of variation for hospital waiting times

The formula for the coefficient of variation ($CV$) is $CV=\frac{s}{\bar{x}}\times100\%$, where $s$ is the standard deviation and $\bar{x}$ is the mean.
For hospital waiting times: $\bar{x} = 80.2$ minutes, $s = 10.5$ minutes.
$CV_{hospital}=\frac{10.5}{80.2}\times100\%$
$CV_{hospital}\approx13.1\%$

Step2: Calculate the coefficient of variation for suspension bridge lengths

For suspension bridge lengths: $\bar{x}$ (not needed for comparison as we can use the ratio of $s$ to a proxy - since we just want to compare the spread relative to the "scale" of the data. But using the formula $CV=\frac{s}{\bar{x}}\times100\%$ (assuming we can consider the data values' magnitude as a scale). However, another way is to note that the standard deviation of hospital waiting times ($s = 10.5$) is a smaller fraction of its mean ($\bar{x}=80.2$) compared to the suspension bridge data.
Alternatively, if we assume for suspension bridge data (values are in feet, $s = 803.2$). The values of bridge lengths (e.g., 4205, 4200 etc.) have a standard deviation that is a larger proportion of the "typical" data values (compared to hospital waiting times where $s = 10.5$ and $\bar{x}=80.2$).
Another approach: Use the range - standard deviation relationship (not exact but for intuition). The hospital waiting time data has a mean of 80.2 and $s = 10.5$ (a relatively "tight" spread around the mean). The suspension bridge data has much larger values and a relatively larger $s$ in terms of the data's magnitude.

Answer:

The set of suspension bridge lengths is more variable.