To calculate the standard deviation for the given data set, we’ll follow these steps:

The values provided are: $1.73, 2.03, 1.89, 2.79, 2.38, 1.08, 1.36, 0.85, 1.77, 2.13$

Step 1: Find the Mean

The mean (average) is calculated by summing all values and dividing by the number of values. $\text{Mean} = \frac{1.73 + 2.03 + 1.89 + 2.79 + 2.38 + 1.08 + 1.36 + 0.85 + 1.77 + 2.13}{10}$

Calculating the sum: $\text{Sum} = 1.73 + 2.03 + 1.89 + 2.79 + 2.38 + 1.08 + 1.36 + 0.85 + 1.77 + 2.13 = 18.01$ $\text{Mean} = \frac{18.01}{10} = 1.801$

Step 2: Calculate the Variance

For each value, subtract the mean and square the result, then find the average of these squared differences.

$\text{Variance} = \frac{(1.73 - 1.801)^2 + (2.03 - 1.801)^2 + (1.89 - 1.801)^2 + \ldots + (2.13 - 1.801)^2}{10}$

Calculating each squared difference: $(1.73 - 1.801)^2 = 0.005041$ $(2.03 - 1.801)^2 = 0.052849$ $(1.89 - 1.801)^2 = 0.007921$ $(2.79 - 1.801)^2 = 0.979681$ $(2.38 - 1.801)^2 = 0.335641$ $(1.08 - 1.801)^2 = 0.518041$ $(1.36 - 1.801)^2 = 0.194481$ $(0.85 - 1.801)^2 = 0.902001$ $(1.77 - 1.801)^2 = 0.000961$ $(2.13 - 1.801)^2 = 0.108241$

Summing these: $\text{Sum of squared differences} = 0.005041 + 0.052849 + 0.007921 + 0.979681 + 0.335641 + 0.518041 + 0.194481 + 0.902001 + 0.000961 + 0.108241 = 3.105858$

$\text{Variance} = \frac{3.105858}{10} = 0.310586$

Step 3: Calculate the Standard Deviation

The standard deviation is the square root of the variance: $\text{Standard Deviation} = \sqrt{0.310586} \approx 0.5575$

Answer:

The standard deviation of the sample data is approximately 0.56 degrees.

Would you like more details or have any further questions?

Here are five additional questions related to this topic:

1. How would the standard deviation change if an outlier were added to the data set?
2. What is the significance of standard deviation in a data set?
3. How would we calculate the variance for a population instead of a sample?
4. Can we use standard deviation to compare the spread of two different data sets?
5. What is the difference between standard deviation and variance?

Tip: Standard deviation provides insight into how much the data varies around the mean; a larger standard deviation indicates more spread.