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The problem involves a set of data values:

- 60, 65, 75, 60, 78, 80, 92, 64

### a. Mean, Median, and Mode

1. **Mean**:
   The mean is calculated as the sum of all data values divided by the number of values.

   \[
   \text{Mean} = \frac{60 + 65 + 75 + 60 + 78 + 80 + 92 + 64}{8}
   \]

2. **Median**:
   To find the median, we first arrange the data in ascending order: 
   
   60, 60, 64, 65, 75, 78, 80, 92
   
   The median is the average of the 4th and 5th values (since there are 8 values, we take the middle two).
   
   \[
   \text{Median} = \frac{65 + 75}{2}
   \]

3. **Mode**:
   The mode is the value that appears most frequently. In this case, the number **60** appears twice, so it is the mode.

### b. \(Q_2\) (Second Quartile):
   
   \(Q_2\) is the median of the data, so the answer to part (b) is the same as the median.

Let me calculate the mean and median next.Here are the calculated values:

- **Mean**: 71.75
- **Median**: 70.0
- **Mode**: 60

### b. \( Q_2 \) (Second Quartile):
Since \( Q_2 \) is the same as the median, \( Q_2 = 70.0 \).

Would you like more details or have any questions?

Here are some related questions for further exploration:
1. How would the mean change if a value in the data set was removed?
2. What happens to the mode if all values are unique?
3. How do you calculate the first quartile \( Q_1 \)?
4. How do you compute the range and interquartile range (IQR) for this data?
5. How does an outlier affect the mean and median?

**Tip**: The median is less sensitive to outliers compared to the mean, making it a better measure of central tendency for skewed distributions.

Consider the following sample data values: 60, 65, 75, 60, 78, 80, 92, 64. Find the mean, median, mode, and Q2.

Learn how to calculate the mean, median, mode, and second quartile (Q2) for the data set: 60, 65, 75, 60, 78, 80, 92, 64. This problem explores key statistical concepts including measures of central tendency and quartiles, suitable for Grades 8-10.

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