Let's go through the data and calculate the standard deviation, as it seems to be where the mistake occurred.

Grades Data:

The grades for the 30 students are as follows:

80, 70, 60, 60, 60
80, 70, 70, 80, 90
70, 70, 70, 70, 90
60, 60, 70, 60, 90
60, 70, 70, 80, 90

Mean:

The mean was correctly calculated as 72.33.

Median:

The median was calculated as 70, which is also correct.

Standard Deviation:

We will now compute the standard deviation.

Steps:

1. Find the mean of the dataLet's go through the data and calculate the standard deviation, as it seems to be where the mistake occurred.

Grades Data:

The grades for the 30 students are as follows:

80, 70, 60, 60, 60
80, 70, 70, 80, 90
70, 70, 70, 70, 90
60, 60, 70, 60, 90
60, 70, 70, 80, 90

Mean:

The mean was correctly calculated as 72.33.

Median:

The median was calculated as 70, which is also correct.

Standard Deviation:

We will now compute the standard deviation.

Steps:

1. Find the mean of the $\mu = 72.33$.
2. Calculate each data point's deviation from the mean, square it, and then find the average of these squared deviations.
3. Take the square root of this average to get the standard deviation.

I'll perform the calculations now to confirm the standard deviation.The mean of the grades is approximately $72.00$, and the correct standard deviation is approximately $10.20$ (rounded to two decimal places).

The error in the previous calculation likely occurred because $11.72$ was an incorrect result. The accurate standard deviation is indeed $10.20$.

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

Here are 5 follow-up questions related to the topic:

1. What is the difference between population and sample standard deviation?
2. How is the median different from the mean in a data set?
3. Why is standard deviation important in statistical analysis?
4. How can outliers affect the standard deviation of a data set?
5. What are other common measures of dispersion besides standard deviation?

Tip: When calculating the standard deviation, make sure to use the correct formula for either population or sample standard deviation based on the data context.