Question

what are the two modal values of the dice shown below?

Explanation:

🆕 New Concept Discovered: Finding the Mode
The value that appears most frequently in a dataset.

Step 1: Count the dots on each die

Let's list the value shown on each of the 9 dice, going row by row from left to right:

• Top row:
• First die: \(6\)
• Second die: \(4\)
• Third die: \(6\)

• Middle row:
• First die: \(2\)
• Second die: \(3\)
• Third die: \(2\)

• Bottom row:
• First die: \(4\)
• Second die: \(2\)
• Third die: \(4\)

Our complete dataset of values is:

$$ \{6, 4, 6, 2, 3, 2, 4, 2, 4\} $$

Step 2: Find the frequency of each value

Now we count how many times each number appears in our list:

• Value \(2\): appears \(3\) times
• Value \(3\): appears \(1\) time
• Value \(4\): appears \(3\) times
• Value \(6\): appears \(2\) times

Step 3: Identify the modal values

The "modal values" (or modes) are the values that appear most frequently.

Both \(2\) and \(4\) appear \(3\) times, which is the highest frequency in this dataset. Since there are two modes, this dataset is bimodal.

Answer:

The two modal values are 2 and 4.