bivariate data 3
Height vs Armspan Bivariate Investigation
Problem: I have noticed that when a person is tall, they seem to have larger armspans than people that are shorter. This seems logical because the height of someone should affect the size of other body parts.
I predict that I will discover a relationship between height and armspan. I also predict that the relationship of these two variables will be moderately strong.
My investigative question is “Is there a relationship between armspan and height?”
PLAN:
We will measure the heights and armspans of all the students in our class. The sample size of 26 students is reasonable for our statistical investigation. Students will be put into groups of 3 and each person in the group will be assigned a specific role such as measuring and recording. My responsibility will be to record the group results and show the data to the teacher who will create a spread sheet from our data. (Others in my group will assist with the taking the measurements. I will then paste the data file (spreadsheet) into NZGrapher to create a scatter graph for analysis.
Manage sources of variation.
To measure height we will use a fixed ruler attached to the wall positioned 1m above the floor. To manage sources of variation each student will take off their shoes and stand straight with their heels against the wall with their back straight. No hats will be worn and hair should be flat, no buns or hair gathered that might give a wrong measurement. Another student will use a flat object to place on the students head to see their height then record it. We will measure to the nearest cm.
To measure armspan we will use a tape measure to measure the distance from the middle finger tip of one hand to the middle finger tip of the other hand, with outstretched arms being held horizontal to the ground.(Not including nail). Each student will place one arm against the wall to help manage sources of variation. Again this was measured to the nearest cm.
Problem: I have noticed that when a person is tall, they seem to have larger armspans than people that are shorter. This seems logical because the height of someone should affect the size of other body parts.
I predict that I will discover a relationship between height and armspan. I also predict that the relationship of these two variables will be moderately strong.
My investigative question is “Is there a relationship between armspan and height?”
PLAN:
We will measure the heights and armspans of all the students in our class. The sample size of 26 students is reasonable for our statistical investigation. Students will be put into groups of 3 and each person in the group will be assigned a specific role such as measuring and recording. My responsibility will be to record the group results and show the data to the teacher who will create a spread sheet from our data. (Others in my group will assist with the taking the measurements. I will then paste the data file (spreadsheet) into NZGrapher to create a scatter graph for analysis.
Manage sources of variation.
To measure height we will use a fixed ruler attached to the wall positioned 1m above the floor. To manage sources of variation each student will take off their shoes and stand straight with their heels against the wall with their back straight. No hats will be worn and hair should be flat, no buns or hair gathered that might give a wrong measurement. Another student will use a flat object to place on the students head to see their height then record it. We will measure to the nearest cm.
To measure armspan we will use a tape measure to measure the distance from the middle finger tip of one hand to the middle finger tip of the other hand, with outstretched arms being held horizontal to the ground.(Not including nail). Each student will place one arm against the wall to help manage sources of variation. Again this was measured to the nearest cm.
Data
Analysis
Looking at my graph, I notice that there is a positive linear relationship between height (cm) and armspan (cm) of the students in 100MAT FEL. This is evident because the trend line has a positive gradient (sloping upwards). The strength of the relationship between height and armspan is moderate, because the majority of the data points are close to the trend line, but some stray a slight way away. This seems to make sense because taller people seem to have longer armspans.
The data is mostly evenly distributed along the trend line, with a group around 168 cm to 175 cm in height. The shortest person has the smallest armspan and the tallest person has the longest armspan. There are three students around the same height of 173 cm who have different armspans. There are 6 students who have about the same armspan of 184/185cm but differ in height considerably (173 to 183 cm).
Conclusion:
The results show that there is a positive and moderate relationship between student height and armspans in 11MAT FEL. This makes sense because people that are taller tend to have longer armspans.
I think that this investigation could have been more reliable if we were to have a larger sample size. For this experiment our class had a sample size of 21 which is lower than the recommended sample size (30). If we had a larger sample size, I would have more confidence in the strength and direction of the relationship. For example, data from 30 or more students could be used to show the relationship of height and armspans across all year 11 students at our school.
I believe that if another year 11 math class were to do this experiment they would have highly similar results. This is because many students are the same size as the students in our class.
Because of this relationship I believe I could predict a students height based on their armspan using the trend line to achieve this. For example,using the data, a student that is 180 cm tall would have an armspan of about 184 cm.
Looking at my graph, I notice that there is a positive linear relationship between height (cm) and armspan (cm) of the students in 100MAT FEL. This is evident because the trend line has a positive gradient (sloping upwards). The strength of the relationship between height and armspan is moderate, because the majority of the data points are close to the trend line, but some stray a slight way away. This seems to make sense because taller people seem to have longer armspans.
The data is mostly evenly distributed along the trend line, with a group around 168 cm to 175 cm in height. The shortest person has the smallest armspan and the tallest person has the longest armspan. There are three students around the same height of 173 cm who have different armspans. There are 6 students who have about the same armspan of 184/185cm but differ in height considerably (173 to 183 cm).
Conclusion:
The results show that there is a positive and moderate relationship between student height and armspans in 11MAT FEL. This makes sense because people that are taller tend to have longer armspans.
I think that this investigation could have been more reliable if we were to have a larger sample size. For this experiment our class had a sample size of 21 which is lower than the recommended sample size (30). If we had a larger sample size, I would have more confidence in the strength and direction of the relationship. For example, data from 30 or more students could be used to show the relationship of height and armspans across all year 11 students at our school.
I believe that if another year 11 math class were to do this experiment they would have highly similar results. This is because many students are the same size as the students in our class.
Because of this relationship I believe I could predict a students height based on their armspan using the trend line to achieve this. For example,using the data, a student that is 180 cm tall would have an armspan of about 184 cm.