- The unique values in the data set are identified from the table as {12, 15, 18, 21}.
- The minimum value is defined as the smallest value among these observations.
- By comparing the values, 12 is found to be the smallest.
- The minimum value is \(\boxed{12}\).
Explanation
- Identifying the Data and Defining the Minimum Value
To determine the minimum value of a data set, we first identify the unique values present in the set. A frequency table shows us how many times each value appears, which helps in understanding the composition of the data set. From the provided table, the unique values present in the data set are 12, 15, 18, and 21. The frequencies (5, 3, 6, and 2) indicate how often each value appears, but they do not influence the identity of the values themselves. The data set, written out, would consist of the value 12 repeated 5 times, 15 repeated 3 times, 18 repeated 6 times, and 21 repeated 2 times. The minimum value of a data set is simply the smallest number present within that set of values.
- Comparing Values and Determining the Minimum
We now compare the set of values {12, 15, 18, 21} to find the smallest one. By comparing these integers:
- 12 is less than 15.
- 15 is less than 18.
- 18 is less than 21.
Since 12 is the smallest value among the numbers present in the data set, it is the minimum value of the data set. Therefore, option 1, which is 12, is the correct choice.
Examples
Imagine you are keeping track of the daily temperatures in your garden over two weeks. You record the temperature each day and then organize your notes into a table showing how many days (frequency) each specific temperature (value) occurred. To find the coldest day of that period, you look at the 'temperature' column in your frequency table and select the lowest number listed, regardless of how many days that temperature lasted. This is a common practice in meteorology and data analysis to quickly identify extremes in a set of observations.