To find the median of a set of numbers, we need to arrange the data in ascending order and then find the middle value.

Given dataTo find the median of a set of numbers, we need to arrange the data in ascending order and then find the middle value.

Given
$6.1, 9.2, 11.1, 5.6, 6.7, 7.7, 6.9, 8.1, 8.1, 6.8, 6.6, 5.9, 7.0, 8.2$

Step 1: Sort the Data

$5.6, 5.9, 6.1, 6.6, 6.7, 6.8, 6.9, 7.0, 7.7, 8.1, 8.1, 8.2, 9.2, 11.1$

Step 2: Find the Middle Value(s)

Since there are 14 data points (an even number), the median will be the average of the two middle values (7th and 8th values).

The 7th and 8th values in the sorted list are: $6.9$ and $7.0$

Step 3: Calculate the Median

$\text{Median} = \frac{6.9 + 7.0}{2} = \frac{13.9}{2} = 6.95$

Answer

The median of this data set is 6.95.

Would you like a breakdown of the steps? Here are related questions for practice:

1. How do you find the median if there’s an odd number of data points?
2. What is the mode of this dataset?
3. How would you find the range of these numbers?
4. Can we calculate the mean of these values?
5. How would the median change if an additional data point was added at 7.5?

Tip: For a set with an even number of elements, the median is the mean of the two central numbers.