Find the standard deviation:

-2.6, 1.9, -4.5, -4.4, .7, -1.5, -3.7, .3

To find the standard deviation of the data set \(-2.6, 1.9, -4.5, -4.4, 0.7, -1.5, -3.7, 0.3\), follow these steps:

### Step 1: Calculate the Mean
First, find the mean (average) of the data set.

\[
\text{Mean} = \frac{-2.6 + 1.9 + (-4.5) + (-4.4) + 0.7 + (-1.5) + (-3.7) + 0.3}{8}
\]

\[
\text{Mean} = \frac{-13.8}{8} = -1.725
\]

### Step 2: Calculate the Squared Differences from the Mean
Next, subtract the mean from each number and square the result:

\[
\begin{align*}
(-2.6 - (-1.725))^2 & = (-0.875)^2 = 0.765625 \\
(1.9 - (-1.725))^2 & = (3.625)^2 = 13.140625 \\
(-4.5 - (-1.725))^2 & = (-2.775)^2 = 7.701025 \\
(-4.4 - (-1.725))^2 & = (-2.675)^2 = 7.155625 \\
(0.7 - (-1.725))^2 & = (2.425)^2 = 5.880625 \\
(-1.5 - (-1.725))^2 & = (0.225)^2 = 0.050625 \\
(-3.7 - (-1.725))^2 & = (-1.975)^2 = 3.900625 \\
(0.3 - (-1.725))^2 & = (2.025)^2 = 4.100625 \\
\end{align*}
\]

### Step 3: Find the Mean of the Squared Differences
Sum the squared differences and divide by the number of data points (since it's a sample, we use \(n-1\)):

\[
\text{Variance} = \frac{0.765625 + 13.140625 + 7.701025 + 7.155625 + 5.880625 + 0.050625 + 3.900625 + 4.100625}{8 - 1}
\]

\[
\text{Variance} = \frac{42.6954}{7} \approx 6.09934
\]

### Step 4: Take the Square Root of the Variance
Finally, the standard deviation is the square root of the variance:

\[
\text{Standard Deviation} = \sqrt{6.09934} \approx 2.4696
\]

### Answer
The standard deviation of the data set is approximately **2.47**.

---

Would you like a more detailed breakdown of any step or have any other questions? 

Here are 5 related questions you might find useful:
1. How do you calculate the variance for a population instead of a sample?
2. What is the significance of the standard deviation in data analysis?
3. How would the standard deviation change if one more data point is added?
4. How is standard deviation different from the range of a data set?
5. Can you calculate the standard deviation for grouped data?

**Tip:** The standard deviation gives insight into how spread out the numbers in a data set are from the mean. A small standard deviation indicates that the numbers are close to the mean, while a large standard deviation indicates that they are spread out.

Learn how to calculate the standard deviation for the data set -2.6, 1.9, -4.5, -4.4, 0.7, -1.5, -3.7, 0.3. Follow a detailed step-by-step solution involving mean calculation, variance computation, and standard deviation formula application. Suitable for students and learners interested in statistics and data analysis.

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