Question

the amount of time required for each of 100 mice to navigate through a maze was recorded. the histogram below shows the distribution of times, in seconds, for the 100 mice. which of the following values is closest to the standard deviation of the 100 times?

Explanation:

Step1: Recall standard - deviation formula

The formula for the standard deviation of a sample is $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$, where $x_{i}$ are the data - points, $\bar{x}$ is the mean, and $n$ is the number of data - points. For a histogram, we first need to estimate the mid - points of each class interval and the frequencies. However, we can also make a rough estimate using the range rule of thumb. The range rule of thumb states that $s\approx\frac{R}{4}$, where $R$ is the range of the data.

Step2: Calculate the range

The range $R$ is the difference between the maximum and minimum values. From the histogram, the minimum value is around $60$ seconds and the maximum value is around $120$ seconds. So, $R=120 - 60=60$ seconds.

Step3: Estimate the standard deviation

Using the range rule of thumb $s\approx\frac{R}{4}$, substituting $R = 60$ into the formula, we get $s\approx\frac{60}{4}=15$ seconds.

Answer:

15 (assuming we are looking for a rough estimate. If we were to calculate precisely, we would need to find the mid - points of each class, frequencies, and use the standard deviation formula).