### Solution:
Let's calculate the different statistical measures (mean score, median score, and modal score) from the given data.
#### (i) Mean Score:
The mean score is the average of all the scores. To find it, add all the scores together and then divide by the number of scores.
Scores Provided: 36, 38, 30, 15, 5
1. Calculate the sum of the scores:
[tex]\[
36 + 38 + 30 + 15 + 5 = 124
\][/tex]
2. Divide the sum by the number of scores (which is 5 in this case):
[tex]\[
\text{Mean score} = \frac{124}{5} = 24.8
\][/tex]
So, the mean score, correct to one decimal place, is 24.8.
#### (ii) Median Score:
The median score is the middle score when all the scores are arranged in ascending order.
1. First, sort the scores in ascending order:
[tex]\[
5, 15, 30, 36, 38
\][/tex]
2. Since there is an odd number of scores (5 scores), the median is the middle score:
[tex]\[
\text{Median score} = 30
\][/tex]
So, the median score is 30.
#### (iii) Modal Score:
The modal score is the score that appears most frequently in the data set.
1. Count the frequency of each score:
- 36 appears 1 time
- 38 appears 1 time
- 30 appears 1 time
- 15 appears 1 time
- 5 appears 1 time
2. Determine the score with the highest frequency:
- Since each score appears only once, we check the highest individual score.
The modal score, in this case, is the highest unique score, which is 36.
### Summary of Calculated Scores:
- Mean score: 24.8
- Median score: 30
- Modal score: 36
