- Define the mode of a set of data.

- Write out instructions for how to calculate the mode of a data set. Then, choose 2 examples below to calculate the mode of the dataset.

[tex]
\[
\begin{array}{|c|c|}
\hline
5, 8, 3, 5, 6, 5, 9, 2, 5 & 12, 15, 7, 9, 7, 12, 7, 18 \\
\hline
& 7, 15 \\
\hline
\end{array}
\]
[/tex]

[tex]
\[
\begin{array}{|c|c|}
\hline
22, 18, 25, 25, 22, 20 & 10, 10, 12, 14, 16, 12 \\
22, 20, 18, 25 & 18, 20, 10, 12 \\
\hline
\end{array}
\]
[/tex]

Sure! Let's break this problem down step-by-step:

1. Definition of the Mode:
- The mode of a set of data is the number that appears most frequently in that data set.

2. Steps to Calculate the Mode of a Data Set:
1. Create a frequency distribution of the data set. This involves counting how many times each number appears in the data set.
2. Identify the number with the highest frequency. This number is the mode of the data set.

3. Examples:

Example 1:
- Data set: [tex]$5, 8, 3, 5, 6, 5, 9, 2, 5$[/tex]
- Step 1: Create a frequency distribution:
- 2 appears 1 time
- 3 appears 1 time
- 5 appears 4 times
- 6 appears 1 time
- 8 appears 1 time
- 9 appears 1 time
- Step 2: Identify the highest frequency:
- The number 5 has the highest frequency of 4 times.
- Therefore, the mode of this data set is 5.

Example 2:
- Data set: [tex]$22, 18, 25, 25, 22, 20, 25, 22, 20, 18$[/tex]
- Step 1: Create a frequency distribution:
- 18 appears 2 times
- 20 appears 2 times
- 22 appears 3 times
- 25 appears 3 times
- Step 2: Identify the highest frequency:
- Both numbers 22 and 25 have the highest frequency of 3 times. However, when multiple numbers have the same highest frequency, there may be more than one mode or it can be considered no unique mode.
- Therefore, the mode of this data set can be considered as both 22 and 25.

These steps ensure that the mode calculation is clear and easy to follow.