Answer :
To determine the median height of the students, follow these steps:
1. List the Heights:
The given heights of the 10 students are: 148 cm, 145 cm, 155 cm, 152 cm, 160 cm, 147 cm, 154 cm, 156 cm, and 158 cm.
2. Sort the Heights in Ascending Order:
When we arrange these from smallest to largest, we get:
145 cm, 147 cm, 148 cm, 152 cm, 154 cm, 155 cm, 156 cm, 158 cm, 160 cm.
3. Determine the Number of Students:
There are 9 heights listed.
4. Calculate the Median:
- The median is the middle value in a list of numbers ordered from smallest to largest. Since we have 9 numbers (which is an odd number), the median will be the middle number in the ordered list.
- To find which number is the median, we use the formula for the position of the median in an ordered list of [tex]\( n \)[/tex] numbers: [tex]\((n + 1) / 2\)[/tex]. In this case, [tex]\( n = 9 \)[/tex], so the position of the median is [tex]\( (9 + 1) / 2 = 10 / 2 = 5 \)[/tex].
- The number at the 5th position in our ordered list is the median.
5. Identify the Median from the Sorted List:
The sorted list is:
145 cm, 147 cm, 148 cm, 152 cm, 154 cm, 155 cm, 156 cm, 158 cm, 160 cm.
- The 5th number in this list is 154 cm.
Therefore, the median height of these students is [tex]\( \boxed{154} \)[/tex] cm.
1. List the Heights:
The given heights of the 10 students are: 148 cm, 145 cm, 155 cm, 152 cm, 160 cm, 147 cm, 154 cm, 156 cm, and 158 cm.
2. Sort the Heights in Ascending Order:
When we arrange these from smallest to largest, we get:
145 cm, 147 cm, 148 cm, 152 cm, 154 cm, 155 cm, 156 cm, 158 cm, 160 cm.
3. Determine the Number of Students:
There are 9 heights listed.
4. Calculate the Median:
- The median is the middle value in a list of numbers ordered from smallest to largest. Since we have 9 numbers (which is an odd number), the median will be the middle number in the ordered list.
- To find which number is the median, we use the formula for the position of the median in an ordered list of [tex]\( n \)[/tex] numbers: [tex]\((n + 1) / 2\)[/tex]. In this case, [tex]\( n = 9 \)[/tex], so the position of the median is [tex]\( (9 + 1) / 2 = 10 / 2 = 5 \)[/tex].
- The number at the 5th position in our ordered list is the median.
5. Identify the Median from the Sorted List:
The sorted list is:
145 cm, 147 cm, 148 cm, 152 cm, 154 cm, 155 cm, 156 cm, 158 cm, 160 cm.
- The 5th number in this list is 154 cm.
Therefore, the median height of these students is [tex]\( \boxed{154} \)[/tex] cm.
