Sure, let's solve the problems step by step.
### Given Data:
- Heights of 7 students in class 9: [tex]\(110 \text{ cm}, 120 \text{ cm}, 90 \text{ cm}, 98 \text{ cm}, 115 \text{ cm}, 112 \text{ cm}\)[/tex]
- Another set of data: [tex]\(35, 40, 58, 70, 45, 27, 86, 65\)[/tex]
### Part (i): Height of the tallest student in class 9
To find the height of the tallest student, we look for the maximum value in the given heights of students.
The heights are: [tex]\(110 \text{ cm}, 120 \text{ cm}, 90 \text{ cm}, 98 \text{ cm}, 115 \text{ cm}, 112 \text{ cm}\)[/tex].
Among these, the tallest height is [tex]\(120 \text{ cm}\)[/tex].
Answer: The height of the tallest student is [tex]\(120 \text{ cm}\)[/tex].
### Part (ii): Height of the shortest student in class 9
To find the height of the shortest student, we look for the minimum value in the given heights of students.
The heights are: [tex]\(110 \text{ cm}, 120 \text{ cm}, 90 \text{ cm}, 98 \text{ cm}, 115 \text{ cm}, 112 \text{ cm}\)[/tex].
Among these, the shortest height is [tex]\(90 \text{ cm}\)[/tex].
Answer: The height of the shortest student is [tex]\(90 \text{ cm}\)[/tex].
### Part (iii): Range of the heights in class 9
The range of the heights is calculated as the difference between the tallest height and the shortest height.
[tex]\[
\text{Range} = \text{Tallest height} - \text{Shortest height} = 120 \text{ cm} - 90 \text{ cm} = 30 \text{ cm}
\][/tex]
Answer: The range of the height in class 9 is [tex]\(30 \text{ cm}\)[/tex].
### Finding the range of the second set of data
The data set is: [tex]\(35, 40, 58, 70, 45, 27, 86, 65\)[/tex].
To find the range:
1. Identify the maximum value in this data set: [tex]\(86\)[/tex].
2. Identify the minimum value in this data set: [tex]\(27\)[/tex].
The range is calculated as:
[tex]\[
\text{Range} = \text{Maximum value} - \text{Minimum value} = 86 - 27 = 59
\][/tex]
Answer: The range of the given data set is [tex]\(59\)[/tex].
To summarize:
- The height of the tallest student is [tex]\(120 \text{ cm}\)[/tex].
- The height of the shortest student is [tex]\(90 \text{ cm}\)[/tex].
- The range of the height in class 9 is [tex]\(30 \text{ cm}\)[/tex].
- The range of the second set of data is [tex]\(59\)[/tex].
