A sample was done, collecting the data below. Calculate the standard deviation, to one decimal place.

x
29
17
2
16
18


To calculate the standard deviation, we can follow these steps:

### Step 1: Find the mean (\(\mu\)).

The mean is the sum of all the data points divided by the number of data points.

\[
\mu = \frac{29 + 17 + 2 + 16 + 18}{5} = \frac{82}{5} = 16.4
\]

### Step 2: Calculate the squared differences from the mean.

For each value \(x_i\), subtract the mean and square the result:

\[
(29 - 16.4)^2 = 12.6^2 = 158.76
\]
\[
(17 - 16.4)^2 = 0.6^2 = 0.36
\]
\[
(2 - 16.4)^2 = (-14.4)^2 = 207.36
\]
\[
(16 - 16.4)^2 = (-0.4)^2 = 0.16
\]
\[
(18 - 16.4)^2 = 1.6^2 = 2.56
\]

### Step 3: Find the average of these squared differences (variance).

\[
\text{Variance} = \frac{158.76 + 0.36 + 207.36 + 0.16 + 2.56}{5} = \frac{369.2}{5} = 73.84
\]

### Step 4: Take the square root of the variance to find the standard deviation.

\[
\text{Standard deviation} = \sqrt{73.84} \approx 8.6
\]

The standard deviation is **8.6**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does standard deviation differ from variance?
2. How would standard deviation change if a new data point was added?
3. What is the significance of a low vs. high standard deviation?
4. How can outliers affect standard deviation?
5. How would we calculate the population standard deviation for this data?

**Tip:** When calculating variance, always make sure you're clear if it's for a sample or a population!

A sample was done, collecting the data below. Calculate the standard deviation, to one decimal place.

x
29
17
2
16
18

Learn how to calculate the standard deviation of a data set, including finding the mean, variance, and final standard deviation. This step-by-step example problem involves the data set {29, 17, 2, 16, 18}. Suitable for high school students.

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