with a mean of 74.33 what is the standard deviation of 
60	60	70	60	90
90	90	90	90	80
70	60	60	80	90
60	80	80	80	80
90	60	70	80	60
60	80	80	60	70

To calculate the standard deviation of the dataset, we follow these steps:

### 1. Mean Calculation
You've already given that the mean of the data is \( \mu = 74.33 \).

### 2. Standard Deviation Formula
The formula for standard deviation \( \sigma \) is:

\[
\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2}
\]

Where:
- \( N \) is the number of data points
- \( x_i \) is each data point
- \( \mu \) is the mean

### 3. Compute the Squared Differences
Let's calculate the squared differences for each data point:

\[
\text{Squared difference} = (x_i - 74.33)^2
\]

Here are the calculations:

| Data Point \(x_i\) | \( x_i - \mu \) | \( (x_i - \mu)^2 \) |
|--------------------|----------------|---------------------|
| 60                 | -14.33         | 205.5089            |
| 60                 | -14.33         | 205.5089            |
| 70                 | -4.33          | 18.7489             |
| 60                 | -14.33         | 205.5089            |
| 90                 | 15.67          | 245.7289            |
| 90                 | 15.67          | 245.7289            |
| 90                 | 15.67          | 245.7289            |
| 90                 | 15.67          | 245.7289            |
| 80                 | 5.67           | 32.1489             |
| 70                 | -4.33          | 18.7489             |
| 60                 | -14.33         | 205.5089            |
| 60                 | -14.33         | 205.5089            |
| 80                 | 5.67           | 32.1489             |
| 90                 | 15.67          | 245.7289            |
| 60                 | -14.33         | 205.5089            |
| 80                 | 5.67           | 32.1489             |
| 80                 | 5.67           | 32.1489             |
| 80                 | 5.67           | 32.1489             |
| 80                 | 5.67           | 32.1489             |
| 90                 | 15.67          | 245.7289            |
| 60                 | -14.33         | 205.5089            |
| 70                 | -4.33          | 18.7489             |
| 80                 | 5.67           | 32.1489             |
| 60                 | -14.33         | 205.5089            |
| 60                 | -14.33         | 205.5089            |
| 80                 | 5.67           | 32.1489             |
| 80                 | 5.67           | 32.1489             |
| 60                 | -14.33         | 205.5089            |
| 70                 | -4.33          | 18.7489             |

### 4. Summing the Squared Differences
Sum of squared differences \( \sum (x_i - \mu)^2 \):

\[
\text{Sum of squared differences} = 4002.66
\]

### 5. Divide by \( N \) (which is 30, since there are 30 data points):

\[
\frac{4002.66}{30} = 133.422
\]

### 6. Take the Square Root

\[
\sigma = \sqrt{133.422} \approx 11.55
\]

### Final Answer:
The standard deviation of the dataset is approximately **11.55**.

Would you like further details or have any questions?

---

Here are 5 related questions to explore:
1. How would the standard deviation change if an additional 100 were added to the dataset?
2. What is the difference between population and sample standard deviation?
3. How does the standard deviation help in understanding the spread of data?
4. Can the standard deviation be zero? If so, in what case?
5. What does it mean when the standard deviation is very large?

**Tip:** Standard deviation gives a measure of how spread out the values in a dataset are, relative to the mean.

with a mean of 74.33 what is the standard deviation of 
60 60 70 60 90
90 90 90 90 80
70 60 60 80 90
60 80 80 80 80
90 60 70 80 60
60 80 80 60 70

Learn how to calculate the standard deviation of a dataset with a mean of 74.33. The data consists of 30 points, and the standard deviation is derived using the formula σ = √(Σ(xi - μ)^2 / N). Detailed calculations are provided, making this suitable for students in Grades 9-12.

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