To find the standard deviation of the given data set:

Data Set:
78, 89, 143, 131, 92, 110, 138, 131, 114, 119, 156, 88, 114, 86, 114, 120, 103, 66, 151, 111, 181, 86, 114, 125, 85, 142, 150, 158, 90, 61, 127, 105, 90, 88, 97, 87

Step 1: Calculate the Mean

The mean (average) is the sum of all values divided by the number of values.

$\text{Mean} = \frac{\sum x}{N}$

Where $\sum x$ is the sum of all values, and $N$ is the number of values.

Step 2: Calculate the Variance

Variance is the average of the squared differences from the Mean.

$\text{Variance} = \frac{\sum (x_i - \mu)^2}{N}$

Where $x_i$ represents each data point, and $\mu$ is the mean.

Step 3: Calculate the Standard Deviation

The standard deviation is the square root of the variance.

$\text{Standard Deviation} = \sqrt{\text{Variance}}$

Let me go ahead and compute this for you.

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I'll perform the calculation now. numpy as np

Data provided by the user

data = [78, 89, 143, 131, 92, 110, 138, 131, 114, 119, 156, 88, 114, 86, 114, 120, 103, 66, 151, 111, 181, 86, 114, 125, 85, 142, 150, 158, 90, 61, 127, 105, 90, 88, 97, 87]

Calculate the standard deviation

std_dev = np.std(data)

std_devThe standard deviation of the given data set is approximately 27.66.

Would you like more details on how this is calculated or have any questions?

Here are some related questions you might find interesting:

1. How does the standard deviation relate to the spread of the data?
2. How does the variance differ from the standard deviation?
3. What does it mean if the standard deviation is high versus low?
4. How would outliers affect the standard deviation?
5. Can the standard deviation be used for non-normally distributed data?

Tip: Standard deviation provides insight into the consistency or variability of a data set. A lower standard deviation means the data points are closer to the mean, while a higher standard deviation indicates more spread out data points.