A certain stock had the following prices for the past five days:

17.80, 15.71, 16.74, 16.21, 15.95

To the nearest hundredth, what is the sample standard deviation of these stock prices?

To calculate the sample standard deviation of the given stock prices, we follow these steps:

1. **Calculate the mean (average) of the dataTo calculate the sample standard deviation of the given stock prices, we follow these steps:

1. **Calculate the mean (average) of the **

\[
\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}} = \frac{17.80 + 15.71 + 16.74 + 16.21 + 15.95}{5}
\]

\[
\text{Mean} = \frac{82.41}{5} = 16.482
\]

2. **Subtract the mean from each data point and square the result (this gives the squared deviations):**

\[
\begin{align*}
(17.80 - 16.482)^2 & = (1.318)^2 = 1.737124 \\
(15.71 - 16.482)^2 & = (-0.772)^2 = 0.595984 \\
(16.74 - 16.482)^2 & = (0.258)^2 = 0.066564 \\
(16.21 - 16.482)^2 & = (-0.272)^2 = 0.073984 \\
(15.95 - 16.482)^2 & = (-0.532)^2 = 0.283024 \\
\end{align*}
\]

3. **Sum the squared deviations:**

\[
\text{Sum of squared deviations} = 1.737124 + 0.595984 + 0.066564 + 0.073984 + 0.283024 = 2.75668
\]

4. **Divide this sum by the number of data points minus 1 (this is called the variance):**

\[
\text{Variance} = \frac{\text{Sum of squared deviations}}{n-1} = \frac{2.75668}{4} = 0.68917
\]

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

\[
\text{Sample Standard Deviation} = \sqrt{0.68917} \approx 0.83009
\]

To the nearest hundredth, the sample standard deviation is:

\[
\boxed{0.83}
\]

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the significance of using the sample standard deviation instead of the population standard deviation?
2. How would the calculation change if the dataset was larger?
3. Can you explain how the variance is interpreted in the context of stock prices?
4. What are the implications of a higher versus lower standard deviation in stock prices?
5. How does sample size affect the accuracy of the standard deviation?

**Tip:** When dealing with datasets, always differentiate between using the sample standard deviation and the population standard deviation. Sample standard deviation is used when dealing with a subset of a population, while population standard deviation is for the entire dataset.

Learn how to calculate the sample standard deviation of a set of stock prices with a step-by-step solution. This problem covers key statistical concepts, including the sample standard deviation formula and variance calculation. Suitable for advanced high school students.

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