The mode for the given data set is 33.
Understanding the Mode in Statistics
The mode is a fundamental measure of central tendency in statistics that identifies the value or values appearing most frequently within a data set. A data set can have one mode (unimodal), multiple modes (multimodal), or no mode if all values occur with the same frequency. Finding the mode is a straightforward process that involves counting the occurrences of each unique number.
Calculating the Mode for the Given Data Set
To determine the mode for the data set: 18, 16, 11, 45, 33, 16, 33, 14, 18, 33, we meticulously count how many times each distinct number appears.
Here is a breakdown of each number and its frequency within the data set:
| Number | Frequency (Count of Occurrences) |
|---|---|
| 11 | 1 |
| 14 | 1 |
| 16 | 2 |
| 18 | 2 |
| 33 | 3 |
| 45 | 1 |
Upon reviewing the frequencies, it is evident that the number 33 appears three times, which is a higher frequency than any other number in the data set. Both 16 and 18 appear twice, while 11, 14, and 45 each appear only once.
Therefore, based on its highest frequency, 33 is identified as the mode of this data set.
