https://file.aiquickdraw.com/mathbot/file/1726154017568sgmpsqt2.jpg

The image shows a data set:

\[ 10, 15, 15, 15, 25, 100 \]

You are asked to calculate how the mean and standard deviation change when the value \(100\) is replaced with \(10\).

### Part A: 

#### Calculating the mean:

1. **Original data set**:
   \[ 10, 15, 15, 15, 25, 100 \]
   The mean is:
   \[
   \text{Mean}_{\text{original}} = \frac{10 + 15 + 15 + 15 + 25 + 100}{6}
   \]

2. **Modified data set** (changing \(100\) to \(10\)):
   \[ 10, 15, 15, 15, 25, 10 \]
   The new mean is:
   \[
   \text{Mean}_{\text{modified}} = \frac{10 + 15 + 15 + 15 + 25 + 10}{6}
   \]

#### Calculating the standard deviation:

Standard deviation measures how much the data points deviate from the mean. Let's calculate it for both sets.

I'll compute these values now.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like to attempt these calculations manually or have me walk you through the steps?

Meanwhile, here are five related questions that might be helpful:

1. What is the formula for calculating the mean of a data set?
2. How do you calculate the standard deviation from a given data set?
3. How does changing an outlier affect the mean of a data set?
4. Why is the mean sensitive to outliers in a data set?
5. What is the difference between the population and sample standard deviation?

**Tip**: When recalculating a data set after replacing an outlier, always check both the mean and standard deviation to see how the distribution has shifted.

After studying the data set [10, 15, 15, 15, 25, 100], it's discovered that the value 100 was meant to be recorded as 10. What happens to the mean and standard deviation of the data set when the 100 is changed to 10?

Explore how changing an outlier in a data set affects the mean and standard deviation. This problem involves a detailed calculation of mean and standard deviation adjustments when an outlier value changes from 100 to 10. Suitable for high school students studying statistics.

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