Find the standard deviation for the given samples. Round non integer results to the nearest tenth. 93, 86, 60, 76, 85, 69, 67

To find the standard deviation of the given sample \(93, 86, 60, 76, 85, 69, 67\), follow these steps:

### Step 1: Calculate the mean
The mean (\(\mu\)) is calculated as the sum of all values divided by the number of values.

\[
\mu = \frac{93 + 86 + 60 + 76 + 85 + 69 + 67}{7} = \frac{536}{7} = 76.6
\]

### Step 2: Find the squared deviations from the mean
Now subtract the mean from each data point and square the result.

\[
(93 - 76.6)^2 = 16.4^2 = 268.96
\]
\[
(86 - 76.6)^2 = 9.4^2 = 88.36
\]
\[
(60 - 76.6)^2 = (-16.6)^2 = 275.56
\]
\[
(76 - 76.6)^2 = (-0.6)^2 = 0.36
\]
\[
(85 - 76.6)^2 = 8.4^2 = 70.56
\]
\[
(69 - 76.6)^2 = (-7.6)^2 = 57.76
\]
\[
(67 - 76.6)^2 = (-9.6)^2 = 92.16
\]

### Step 3: Calculate the variance
The variance is the average of these squared deviations. Since it's a sample, use \(n - 1\) as the denominator.

\[
\text{Variance} = \frac{268.96 + 88.36 + 275.56 + 0.36 + 70.56 + 57.76 + 92.16}{7 - 1} = \frac{853.72}{6} = 142.29
\]

### Step 4: Find the standard deviation
The standard deviation is the square root of the variance:

\[
\text{Standard deviation} = \sqrt{142.29} \approx 11.9
\]

So, the standard deviation is approximately **11.9**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the standard deviation for a population instead of a sample?
2. What is the difference between variance and standard deviation?
3. How does standard deviation relate to data spread?
4. Can the standard deviation ever be negative?
5. What is the effect of an outlier on the standard deviation?

**Tip:** Standard deviation is sensitive to extreme values, so always check for outliers when interpreting data spread!

Find the standard deviation for the given samples. Round non-integer results to the nearest tenth. 93, 86, 60, 76, 85, 69, 67

Learn how to calculate the standard deviation for the sample 93, 86, 60, 76, 85, 69, 67. This step-by-step guide covers statistical concepts such as mean, variance, and standard deviation, and is suitable for students in Grades 9-12.

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