Sure, let's address each part of the question step by step.
### Part (i) - Mode
The mode is the number that appears most frequently in a data set.
From the table:
- The frequency of the number 2 is 3.
- The frequency of the number 3 is 2.
- The frequency of the number 4 is 6.
- The frequency of the number 5 is 4.
- The frequency of the number 6 is 5.
We see that the number 4 appears the most frequently with a frequency of 6. Thus, the mode is:
[tex]\[ \boxed{4} \][/tex]
### Part (ii) - Mean
The mean (average) is calculated by dividing the sum of all numbers by the total count of numbers.
First, let's calculate the total number of spins and the weighted sum of the numbers:
- Total number of spins:
[tex]\[
3 + 2 + 6 + 4 + 5 = 20
\][/tex]
- Weighted sum of the numbers:
[tex]\[
(3 \times 2) + (2 \times 3) + (6 \times 4) + (4 \times 5) + (5 \times 6)
\][/tex]
[tex]\[
= 6 + 6 + 24 + 20 + 30
\][/tex]
[tex]\[
= 86
\][/tex]
Now, we calculate the mean by dividing the weighted sum by the total number of spins:
[tex]\[
\text{Mean} = \frac{86}{20} = 4.3
\][/tex]
Thus, the mean is:
[tex]\[ \boxed{4.3} \][/tex]
