Let's address each part of the question step by step:
### 1.1.1 Arrange the girls' scores in descending order
The girls' scores in descending order are:
[tex]\[568, 99, 98, 89, 79, 75, 75, 75, 67, 59, 49, 39, 38, 11, 10, 9, 7, 6, 5, 5, 4, 3, 2, 1\][/tex]
### 1.1.2 Write down the girls' modal score
The modal score is the most frequently occurring score in the dataset. For the girls, the modal score is:
[tex]\[75\][/tex]
(since 75 appears three times in the list of girls' scores).
### 1.1.3 Calculate the boys' mean score
The mean score is calculated by summing all the scores and dividing by the number of scores.
Sum of boys' scores:
[tex]\[48 + 56 + 57 + 58 + 65 + 66 + 66 + 68 + 73 + 77 + 78 + 81 + 85 + 96 = 974\][/tex]
Number of boys:
[tex]\[14\][/tex]
Mean score:
[tex]\[\frac{974}{14} = 69.57142857142857 \approx 69.57\%\][/tex]
### 1.1.4 Calculate the boys' median score
The median score is the middle value in a sorted list of scores. If the list has an even number of observations, the median is the average of the two middle numbers.
Sorted boys' scores:
[tex]\[48, 56, 57, 58, 65, 66, 66, 68, 73, 77, 78, 81, 85, 96\][/tex]
Number of boys (n):
[tex]\[14\][/tex]
Since the number of scores is even, the median is the average of the 7th and 8th scores. In the sorted list, the 7th score is 66 and the 8th score is 68.
Median score:
[tex]\[\frac{66 + 68}{2} = 67.0\][/tex]
### 1.1.5 Determine the range of the girls' scores
The range is the difference between the maximum and minimum scores.
Maximum girls' score:
[tex]\[568\][/tex]
Minimum girls' score:
[tex]\[1\][/tex]
Range:
[tex]\[568 - 1 = 567\][/tex]
### 1.1.6 Determine the probability that a boy chosen at random scored more than 75% in the test. Write your answer in percentage form.
Firstly, we identify the boys' scores that are greater than 75.
Boys' scores above 75:
[tex]\[77, 78, 81, 85, 96\][/tex]
Number of boys scoring above 75:
[tex]\[5\][/tex]
Total number of boys:
[tex]\[14\][/tex]
Probability:
[tex]\[\frac{5}{14} \approx 0.35714285714285715\][/tex]
Percentage form:
[tex]\[0.35714285714285715 \times 100 = 35.71\%\][/tex]
### Summary of Solutions:
1. Girls' scores in descending order: 568, 99, 98, 89, 79, 75, 75, 75, 67, 59, 49, 39, 38, 11, 10, 9, 7, 6, 5, 5, 4, 3, 2, 1
2. Girls' modal score: 75
3. Boys' mean score: 69.57%
4. Boys' median score: 67.0
5. Range of the girls' scores: 567
6. Probability that a randomly chosen boy scored more than 75%: 35.71%
