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Let's solve the question.

### Given Data Set:
Original data set for DVD movies owned:
\[ 75, 78, 81, 90, 95, 97, 100 \]

Suppose the number **75** changes to **82**.

### Step 1: Calculate the Mean Before and After the Change

1. **Mean Before the Change**:
   \[
   \text{Mean} = \frac{75 + 78 + 81 + 90 + 95 + 97 + 100}{7}
   = \frac{616}{7} = 88
   \]

2. **Mean After the Change**:
   Replace 75 with 82 in the data set:
   \[ 82, 78, 81, 90, 95, 97, 100 \]
   \[
   \text{New Mean} = \frac{82 + 78 + 81 + 90 + 95 + 97 + 100}{7}
   = \frac{623}{7} = 89
   \]

### Step 2: Calculate the Median Before and After the Change

The median is the middle value when the data is ordered.

1. **Median Before the Change**:
   Ordered dataLet's solve the question.

### Given Data Set:
Original data set for DVD movies owned:
\[ 75, 78, 81, 90, 95, 97, 100 \]

Suppose the number **75** changes to **82**.

### Step 1: Calculate the Mean Before and After the Change

1. **Mean Before the Change**:
   \[
   \text{Mean} = \frac{75 + 78 + 81 + 90 + 95 + 97 + 100}{7}
   = \frac{616}{7} = 88
   \]

2. **Mean After the Change**:
   Replace 75 with 82 in the data set:
   \[ 82, 78, 81, 90, 95, 97, 100 \]
   \[
   \text{New Mean} = \frac{82 + 78 + 81 + 90 + 95 + 97 + 100}{7}
   = \frac{623}{7} = 89
   \]

### Step 2: Calculate the Median Before and After the Change

The median is the middle value when the data is ordered.

1. **Median Before the Change**:
   Ordered  \( 75, 78, 81, 90, 95, 97, 100 \)
   Middle value (4th position): **90**

2. **Median After the Change**:
   Ordered dataLet's solve the question.

### Given Data Set:
Original data set for DVD movies owned:
\[ 75, 78, 81, 90, 95, 97, 100 \]

Suppose the number **75** changes to **82**.

### Step 1: Calculate the Mean Before and After the Change

1. **Mean Before the Change**:
   \[
   \text{Mean} = \frac{75 + 78 + 81 + 90 + 95 + 97 + 100}{7}
   = \frac{616}{7} = 88
   \]

2. **Mean After the Change**:
   Replace 75 with 82 in the data set:
   \[ 82, 78, 81, 90, 95, 97, 100 \]
   \[
   \text{New Mean} = \frac{82 + 78 + 81 + 90 + 95 + 97 + 100}{7}
   = \frac{623}{7} = 89
   \]

### Step 2: Calculate the Median Before and After the Change

The median is the middle value when the data is ordered.

1. **Median Before the Change**:
   Ordered  \( 75, 78, 81, 90, 95, 97, 100 \)
   Middle value (4th position): **90**

2. **Median After the Change**:
   Ordered  \( 78, 81, 82, 90, 95, 97, 100 \)
   Middle value (4th position): **90**

### Conclusion
- **Mean Before the Change** = 88, **Mean After the Change** = 89
- **Median Before the Change** = 90, **Median After the Change** = 90

### Correct Answer:
The correct choice is:
- **Mean before the change = 88. Mean after the change = 89**
- **Median before the change = 90. Median after the change = 90**

Would you like further details or have any questions?

### Related Questions:
1. How is the mean affected when a single data point in a set is changed?
2. What is the difference between mean and median, and how do they respond to changes in data?
3. How can outliers affect the mean and median of a data set?
4. Why is it important to order data before finding the median?
5. How would adding a new data point affect the mean and median?

### Tip:
When calculating the mean, small changes in individual data values can shift the mean, but the median is often more stable since it depends on the middle position, not individual values.

The data set below provides the number of DVD movies owned by 7 students: 75, 78, 81, 90, 95, 97, 100. Suppose that the number 75 from this data set changed to 82. What is the mean before the change? After the change? What is the median before the change? After the change?

Calculate the mean and median of a data set before and after changing one value. This question involves a data set of DVD movies owned by 7 students. Learn how to find the mean and median and understand their changes when one value is updated.

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