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.