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To find the standard deviation of Billy's test scores, we will follow these steps:

### Test Scores:
Billy's scores are: 89, 88, 93, 90, and 81.

### Step 1: Find the Mean
The mean (average) is the sum of the scores divided by the number of tests:
\[
\text{Mean} = \frac{89 + 88 + 93 + 90 + 81}{5} = \frac{441}{5} = 88.2
\]

### Step 2: Find the Squared Differences from the Mean
For each score, subtract the mean and square the result:
- For 89: \((89 - 88.2)^2 = (0.8)^2 = 0.64\)
- For 88: \((88 - 88.2)^2 = (-0.2)^2 = 0.04\)
- For 93: \((93 - 88.2)^2 = (4.8)^2 = 23.04\)
- For 90: \((90 - 88.2)^2 = (1.8)^2 = 3.24\)
- For 81: \((81 - 88.2)^2 = (-7.2)^2 = 51.84\)

### Step 3: Find the Variance
The variance is the average of these squared differences:
\[
\text{Variance} = \frac{0.64 + 0.04 + 23.04 + 3.24 + 51.84}{5} = \frac{78.8}{5} = 15.76
\]

### Step 4: Find the Standard Deviation
The standard deviation is the square root of the variance:
\[
\text{Standard Deviation} = \sqrt{15.76} \approx 3.97
\]

So, the correct answer is **3.97**.

Would you like any further clarification? Here are some related questions:
1. How do you calculate variance from a set of data?
2. What is the difference between population and sample standard deviation?
3. How does a larger or smaller standard deviation affect data distribution?
4. Can standard deviation be negative? Why or why not?
5. How would you calculate the standard deviation for a larger dataset?

**Tip:** To understand the spread of data, the standard deviation gives a better sense of how scores differ from the mean, while variance is useful for mathematical analysis but harder to interpret directly in terms of the original data units.

Billy took 5 tests in his math class. He scored an 89, 88, 93, 90, and 81. What is the standard deviation of his grades in these tests? If necessary, round to the nearest hundredth.

Learn how to calculate the standard deviation of Billy's test scores (89, 88, 93, 90, and 81) step by step. This problem covers key concepts in statistics, including mean, variance, and standard deviation. Suitable for students in Grades 9-11.

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