Answer :
Certainly! Let's go through each part of the question step-by-step.
### 1.1.1 Arrange the girls' scores in descending order. (2 marks)
First, let's list the given girls' scores:
[tex]\[38, 75, 49, 79, 39, 99, 56, 67, 98, 89, 59, 75, 75\][/tex]
Now, arrange these scores in descending order:
[tex]\[99, 98, 89, 79, 75, 75, 75, 67, 59, 56, 49, 39, 38\][/tex]
Answer:
[tex]\[99, 98, 89, 79, 75, 75, 75, 67, 59, 56, 49, 39, 38\][/tex]
### 1.1.2 Write down the girls' modal score. (2 marks)
The modal score is the score that appears most frequently in the list of scores.
Here are the counts for each score:
- 99 appears 1 time
- 98 appears 1 time
- 89 appears 1 time
- 79 appears 1 time
- 75 appears 3 times
- 67 appears 1 time
- 59 appears 1 time
- 56 appears 1 time
- 49 appears 1 time
- 39 appears 1 time
- 38 appears 1 time
The score that appears most frequently is [tex]\(75\)[/tex].
Answer:
The girls' modal score is [tex]\(75\)[/tex].
### 1.1.3 Calculate the boys' mean score. (2 marks)
The boys' scores are:
[tex]\[48, 56, 57, 58, 65, 66, 66, 68, 73, 77, 78, 81, 85, 96\][/tex]
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' scores:
[tex]\[14\][/tex]
Mean score:
[tex]\[\frac{974}{14} \approx 69.57\][/tex]
Answer:
The boys' mean score is approximately [tex]\(69.57\)[/tex].
### 1.1.4 Calculate the boys' median score. (2 marks)
To find the median, we need to arrange the boys' scores in ascending order and then find the middle score.
The boys' scores in ascending order:
[tex]\[48, 56, 57, 58, 65, 66, 66, 68, 73, 77, 78, 81, 85, 96\][/tex]
Since there are 14 scores (an even number), the median is the average of the 7th and 8th scores.
7th score is [tex]\(66\)[/tex] and 8th score is [tex]\(68\)[/tex].
Median score:
[tex]\[\frac{66 + 68}{2} = 67\][/tex]
Answer:
The boys' median score is [tex]\(67\)[/tex].
### 1.1.5 Determine the range of the girls' score. (2 marks)
The range is calculated by subtracting the smallest score from the largest score.
From the ordered girls' scores:
Smallest score = [tex]\(38\)[/tex]
Largest score = [tex]\(99\)[/tex]
Range:
[tex]\[99 - 38 = 61\][/tex]
Answer:
The range of the girls' score is [tex]\(61\)[/tex].
### 1.1.6 Determine the probability that a boy chosen at random scores more than 75% in the test. Write your answer in percentage form. (5 marks)
We need to count the number of boys with scores greater than 75 and then find the probability in percentage form.
The boys' scores are:
[tex]\[48, 56, 57, 58, 65, 66, 66, 68, 73, 77, 78, 81, 85, 96\][/tex]
Scores greater than 75 are:
[tex]\[77, 78, 81, 85, 96\][/tex]
Number of boys scoring more than 75 is [tex]\(5\)[/tex].
Total number of boys' scores is [tex]\(14\)[/tex].
Probability:
[tex]\[\frac{5}{14} \times 100 \approx 35.71\][/tex]
Answer:
The probability that a boy chosen at random scores more than 75% in the test is approximately [tex]\(35.71\%\)[/tex].
### 1.1.1 Arrange the girls' scores in descending order. (2 marks)
First, let's list the given girls' scores:
[tex]\[38, 75, 49, 79, 39, 99, 56, 67, 98, 89, 59, 75, 75\][/tex]
Now, arrange these scores in descending order:
[tex]\[99, 98, 89, 79, 75, 75, 75, 67, 59, 56, 49, 39, 38\][/tex]
Answer:
[tex]\[99, 98, 89, 79, 75, 75, 75, 67, 59, 56, 49, 39, 38\][/tex]
### 1.1.2 Write down the girls' modal score. (2 marks)
The modal score is the score that appears most frequently in the list of scores.
Here are the counts for each score:
- 99 appears 1 time
- 98 appears 1 time
- 89 appears 1 time
- 79 appears 1 time
- 75 appears 3 times
- 67 appears 1 time
- 59 appears 1 time
- 56 appears 1 time
- 49 appears 1 time
- 39 appears 1 time
- 38 appears 1 time
The score that appears most frequently is [tex]\(75\)[/tex].
Answer:
The girls' modal score is [tex]\(75\)[/tex].
### 1.1.3 Calculate the boys' mean score. (2 marks)
The boys' scores are:
[tex]\[48, 56, 57, 58, 65, 66, 66, 68, 73, 77, 78, 81, 85, 96\][/tex]
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' scores:
[tex]\[14\][/tex]
Mean score:
[tex]\[\frac{974}{14} \approx 69.57\][/tex]
Answer:
The boys' mean score is approximately [tex]\(69.57\)[/tex].
### 1.1.4 Calculate the boys' median score. (2 marks)
To find the median, we need to arrange the boys' scores in ascending order and then find the middle score.
The boys' scores in ascending order:
[tex]\[48, 56, 57, 58, 65, 66, 66, 68, 73, 77, 78, 81, 85, 96\][/tex]
Since there are 14 scores (an even number), the median is the average of the 7th and 8th scores.
7th score is [tex]\(66\)[/tex] and 8th score is [tex]\(68\)[/tex].
Median score:
[tex]\[\frac{66 + 68}{2} = 67\][/tex]
Answer:
The boys' median score is [tex]\(67\)[/tex].
### 1.1.5 Determine the range of the girls' score. (2 marks)
The range is calculated by subtracting the smallest score from the largest score.
From the ordered girls' scores:
Smallest score = [tex]\(38\)[/tex]
Largest score = [tex]\(99\)[/tex]
Range:
[tex]\[99 - 38 = 61\][/tex]
Answer:
The range of the girls' score is [tex]\(61\)[/tex].
### 1.1.6 Determine the probability that a boy chosen at random scores more than 75% in the test. Write your answer in percentage form. (5 marks)
We need to count the number of boys with scores greater than 75 and then find the probability in percentage form.
The boys' scores are:
[tex]\[48, 56, 57, 58, 65, 66, 66, 68, 73, 77, 78, 81, 85, 96\][/tex]
Scores greater than 75 are:
[tex]\[77, 78, 81, 85, 96\][/tex]
Number of boys scoring more than 75 is [tex]\(5\)[/tex].
Total number of boys' scores is [tex]\(14\)[/tex].
Probability:
[tex]\[\frac{5}{14} \times 100 \approx 35.71\][/tex]
Answer:
The probability that a boy chosen at random scores more than 75% in the test is approximately [tex]\(35.71\%\)[/tex].
