Calculating Mean of Mode and Median

The problem asks us to find the mean of the mode and the median for the given dataset. First, we need to identify the mode and the median from the data.

Given Data: 15, 3, 8, 7, 6, 5, 5, 7, 18, 7

Finding the Mode

The mode is the value that appears most frequently in the dataset.

1. Count the occurrences of each number:
   • 3: 1 time
   • 5: 2 times
   • 6: 1 time
   • 7: 3 times
   • 8: 1 time
   • 15: 1 time
   • 18: 1 time
2. The number 7 appears 3 times, which is more than any other number.

Mode = 7

Finding the Median

The median is the middle value of a dataset when it is ordered. If there's an even number of observations, the median is the average of the two middle values.

1. Arrange the data in ascending order:

   3, 5, 5, 6, 7, 7, 7, 8, 15, 18

2. Count the total number of data points (n). Here, n = 10.
3. Since n is even, the median is the average of the \(\frac{n}{2}\)-th and \((\frac{n}{2} + 1)\)-th values.

   \(\frac{10}{2} = 5\)-th term

   \(\frac{10}{2} + 1 = 6\)-th term

4. The 5th term is 7 and the 6th term is 7.
5. Calculate the average of these two middle values:

   Median = \(\frac{7 + 7}{2} = \frac{14}{2} = 7\)

Median = 7

Calculating the Mean of Mode and Median

Finally, we calculate the mean of the mode (7) and the median (7).

Mean = \(\frac{\text{Mode} + \text{Median}}{2}\)

Mean = \(\frac{7 + 7}{2} = \frac{14}{2} = 7\)

The mean of the mode and the median is 7.