Sure, let's break down each part of the question step-by-step:
### 1.1.1 Arrange the girls' scores in descending order.
To arrange the girls' scores in descending order, we start by listing the scores:
[tex]\[38, 11, 75, 5, 49, 9, 79, 4, 39, 10, 99, 1, 568, 67, 6, 98, 7, 89, 3, 59, 7, 75, 5, 75\][/tex]
Now, we sort these scores from the highest to the lowest:
[tex]\[568, 99, 98, 89, 79, 75, 75, 75, 67, 59, 49, 39, 38, 11, 10, 9, 7, 7, 6, 5, 5, 4, 3, 1\][/tex]
### 1.1.2 Write down the girls' modal score.
The modal score is the score that appears the most frequently. In the sorted list:
[tex]\[568, 99, 98, 89, 79, 75, 75, 75, 67, 59, 49, 39, 38, 11, 10, 9, 7, 7, 6, 5, 5, 4, 3, 1\][/tex]
You can see that the score 75 appears three times, which is more frequent than any other score.
Thus, the girls' modal score is [tex]\(75\)[/tex].
### 1.1.3 Calculate the boys' mean score.
To calculate the mean score, we add up all the boys' scores and then divide by the number of scores. The boys' scores are:
[tex]\[48, 56, 57, 58, 65, 66, 66, 68, 73, 77, 78, 81, 85, 96\][/tex]
First, add them up:
[tex]\[48 + 56 + 57 + 58 + 65 + 66 + 66 + 68 + 73 + 77 + 78 + 81 + 85 + 96 = 974\][/tex]
There are 14 scores, so we divide the total by 14:
[tex]\[
\text{Mean score} = \frac{974}{14} \approx 69.57
\][/tex]
So, the boys' mean score is approximately [tex]\(69.57\)[/tex].
### 1.1.4 Calculate the boys' median score.
To find the median score, we first need to sort the boys' scores in ascending order:
[tex]\[48, 56, 57, 58, 65, 66, 66, 68, 73, 77, 78, 81, 85, 96\][/tex]
There are 14 scores, so the median is the average of the 7th and 8th scores. The 7th and 8th scores are:
66 and 68
Thus, the median is:
[tex]\[
\text{Median score} = \frac{66 + 68}{2} = 67
\][/tex]
So, the boys' median score is [tex]\(67\)[/tex].
### 1.1.5 Determine the range of the girls' scores.
The range is found by subtracting the smallest score from the largest score. Looking at the sorted list:
[tex]\[568, 99, 98, 89, 79, 75, 75, 75, 67, 59, 49, 39, 38, 11, 10, 9, 7, 7, 6, 5, 5, 4, 3, 1\][/tex]
The largest score is [tex]\(568\)[/tex] and the smallest score is [tex]\(1\)[/tex]. So the range is:
[tex]\[
\text{Range} = 568 - 1 = 567
\][/tex]
Thus, the range of the girls' scores is [tex]\(567\)[/tex].
### 1.1.6 Determine the probability that a boy chosen at random scores 75 (1) in the test.
First, we note that none of the boys' scores are 75. The boys' scores are:
[tex]\[48, 56, 57, 58, 65, 66, 66, 68, 73, 77, 78, 81, 85, 96\][/tex]
No score of 75 is present.
The total number of boys is 14, and the number of boys scoring 75 is 0. The probability is:
[tex]\[
\text{Probability} = \frac{\text{Number of boys scoring 75}}{\text{Total number of boys}} \times 100\% = \frac{0}{14} \times 100\% = 0\%
\][/tex]
Therefore, the probability that a randomly chosen boy scores 75 is [tex]\(0\%\)[/tex].
