The mode of a data set refers to the value or values that appear most frequently in the set. In other words, it is the value(s) that occur with the highest frequency. To find the mode of a data set, we need to count how many times each value appears and then identify the one(s) with the highest frequency.
Let's apply this concept to the given data set: 8, 20, 32, 39, 44, 20, 63.
First, we need to count how many times each value appears:
- The value 8 appears once.
- The value 20 appears twice.
- The value 32 appears once.
- The value 39 appears once.
- The value 44 appears once.
- The value 63 appears once.
From this count, we can see that the value 20 appears the most frequently, with a frequency of 2. Therefore, the mode of this data set is 20.
It's important to note that in some data sets, there may be multiple values with the same highest frequency. In such cases, the data set is said to have multiple modes. However, in this particular data set, 20 is the only value that appears with the highest frequency.