The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes; mean = 114.15):
118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118.
What is the variance?

Multiple Choice

103


23.62


557.97


128.8


115

To find the variance of the given data, we follow these steps:

1. **Step 1: Compute the mean (already given as 114.15 minutes).**

2. **Step 2: Subtract the mean from each data point to find the deviations.**
   \[
   \text{Deviations} = \{118 - 114.15, 124 - 114.15, 108 - 114.15, \dots \}
   \]

3. **Step 3: Square each deviation to eliminate negative values.**

4. **Step 4: Sum the squared deviations.**

5. **Step 5: Divide the sum of the squared deviations by \(n-1\) (since this is a sample variance, \(n = 13\)).**

Let's calculate this step by step.The variance of the given data is approximately **557.97**.

Would you like more details, or do you have any other questions?

Here are 5 related questions to explore:

1. What is the standard deviation for this data set?
2. How does the variance compare to the standard deviation in interpretation?
3. What effect does an outlier like the value "45" have on the variance?
4. How would the variance change if more patrons were surveyed?
5. What is the difference between population variance and sample variance?

**Tip:** The standard deviation is the square root of the variance and provides a more interpretable measure of spread in the same units as the data.

The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes; mean = 114.15): 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118. What is the variance?

Discover how to calculate the variance for the wait times at a roller coaster using sample data from 13 patrons. This problem involves statistical concepts such as variance, sample data analysis, and the formula for variance. The recorded times range from 45 to 148 minutes with a mean of 114.15 minutes.

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