The Vetrone family members are all Cincinnati Reds baseball fans. They went to five games last season. The cost of each game, including parking, tickets, and food, is listed below.
$266, $201, $197, $188, $162   what the standard deviation

To calculate the standard deviation of the costs of the five games, we'll follow these steps:

1. **Calculate the mean (average) of the data set:**

\[
\text{Mean} = \frac{\sum \text{costs}}{N} = \frac{266 + 201 + 197 + 188 + 162}{5} = \frac{1014}{5} = 202.8
\]

2. **Find the squared differences from the mean for each cost:**

\[
(266 - 202.8)^2 = 4026.24
\]
\[
(201 - 202.8)^2 = 3.24
\]
\[
(197 - 202.8)^2 = 33.64
\]
\[
(188 - 202.8)^2 = 220.84
\]
\[
(162 - 202.8)^2 = 1668.84
\]

3. **Calculate the average of these squared differences (variance):**

\[
\text{Variance} = \frac{4026.24 + 3.24 + 33.64 + 220.84 + 1668.84}{5} = \frac{5952.8}{5} = 1190.56
\]

4. **Take the square root of the variance to get the standard deviation:**

\[
\text{Standard Deviation} = \sqrt{1190.56} \approx 34.52
\]

So, the standard deviation of the costs is approximately **$34.52**.

Would you like any details or have any questions?

Here are 5 related questions:
1. How is standard deviation used in real-world scenarios?
2. What is the difference between standard deviation and variance?
3. How does the standard deviation change if one of the costs increases significantly?
4. What is the significance of a low standard deviation in a data set?
5. How can the standard deviation be interpreted in terms of the cost variability of the games?

**Tip:** Understanding standard deviation helps you measure the spread of data points around the mean, which is crucial in assessing variability in data sets.

Learn how to calculate the standard deviation of costs for five Cincinnati Reds baseball games, including parking, tickets, and food. Understand the variance and mean calculations involved. Suitable for high school students studying statistics.

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