To find the mean, or average, of Josh's dice rolls, we need to follow these steps:
1. Record the results and their frequencies:
The dice outcome frequencies are as follows:
- Dice roll 1: 15 times
- Dice roll 2: 18 times
- Dice roll 3: 14 times
- Dice roll 4: 16 times
- Dice roll 5: 19 times
- Dice roll 6: 18 times
2. Calculate the total number of rolls:
To get the total number of rolls, we sum up all the frequencies:
[tex]\[
15 + 18 + 14 + 16 + 19 + 18 = 100
\][/tex]
3. Calculate the total sum of all dice results:
Multiply each dice roll by its frequency and add them together:
[tex]\[
(1 \cdot 15) + (2 \cdot 18) + (3 \cdot 14) + (4 \cdot 16) + (5 \cdot 19) + (6 \cdot 18)
\][/tex]
This gives us:
[tex]\[
15 + 36 + 42 + 64 + 95 + 108 = 360
\][/tex]
4. Compute the mean (average):
The mean is calculated by dividing the total sum of all dice results by the total number of rolls:
[tex]\[
\text{Mean} = \frac{\text{Total Sum}}{\text{Total Rolls}} = \frac{360}{100} = 3.6
\][/tex]
Therefore, the mean, or average, result of Josh's dice rolls is [tex]\( \boxed{3.6} \)[/tex].
