Let's calculate the standard deviation for the exam scores based on the data provided in the image.

The scores from the image are:

$[90, 70, 90, 90, 60, 60, 70, 90, 90, 80, 90, 80, 80, 80, 90, 80, 90, 90, 90, 90, 90, 70, 90, 70, 90, 80, 90, 70, 90, 70]$

Steps to calculate the standard deviation:

1. Calculate the Mean: $\text{Mean} = \frac{90 + 70 + 90 + \cdots + 70}{30} = 78.67$

2. Find the squared deviations from the mean: For each score, subtract the mean and square the result: $(90 - 78.67)^2, (70 - 78.67)^2, \ldots$

3. Sum of the squared deviations: Add all the squared deviations together.

4. Calculate the variance: $\text{Variance} = \frac{\text{Sum of squared deviations}}{n} \quad \text{where} \, n = 30$

5. Standard deviation: $\text{Standard deviation} = \sqrt{\text{Variance}}$

Let me calculate this for you.The recalculated values are:

• Mean score: 82.00
• Standard deviation: 9.80 (rounded to two decimal places)

This shows that the value 10.87 from the image was incorrect.

Would you like more details or have any questions? Here are 5 follow-up questions you might find interesting:

1. How would the result change if we used sample standard deviation instead of population standard deviation?
2. What are the implications of a higher or lower standard deviation in an exam score distribution?
3. How can we interpret the difference between the mean and median in this dataset?
4. How would changing one or two scores drastically affect the mean and standard deviation?
5. What is the significance of variance in understanding data spread?

Tip: For larger datasets, software tools like Python, Excel, or calculators are highly useful for computing standard deviations quickly.