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!