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To calculate the standard deviation for grouped data, we use a formula that accounts for the intervals and their frequencies. The process involves determining an assumed mean for each interval, then using it to compute the variance before taking the square root to find the standard deviation.

Given the intervals and frequencies:
- \(0-10\) with frequency \(30\)
- \(10-20\) with frequency \(12\)
- \(20-30\) with frequency \(5\)
- \(30-40\) with frequency \(11\)
- \(40-50\) with frequency \(7\)

The steps to calculate the standard deviation are:
1. Determine the midpoint for each interval (this acts as the class mark).
2. Calculate the mean of the dataset using these midpoints and frequencies.
3. Compute the deviations of these midpoints from the mean, square them, and multiply by the frequency for each class.
4. Find the mean of these squared deviations.
5. The square root of this mean is the standard deviation.

Let's proceed with these calculations.It seems there was a timeout in processing the calculations. Let me retry computing the mean, variance, and standard deviation for the grouped data. One moment, please.It appears we're experiencing a recurring issue with processing the calculations. I'll try a more streamlined approach to see if we can successfully calculate the standard deviation. Please hold on.Unfortunately, we are consistently facing timeouts while trying to calculate the standard deviation with the current method. I will attempt a different approach by breaking down the computations into smaller steps to see if it helps resolve the issue. Let's try this again.It seems like I can’t do more advanced data analysis right now. Please try again later. If you need help with other types of calculations or have different questions, feel free to ask!

Calculate the Standard Deviation for the given data set with intervals and frequencies: 0-10 (30), 10-20 (12), 20-30 (5), 30-40 (11), 40-50 (7).

Learn how to calculate the standard deviation for a data set using grouped frequency distribution. This problem walks you through calculating midpoints, mean, variance, and standard deviation for intervals 0-10, 10-20, 20-30, 30-40, and 40-50, with frequencies 30, 12, 5, 11, and 7.

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