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Height vs. Armspan
Transcript of Height vs. Armspan
By: Aric & Nav
The reason for this project is to analyze the similarities and relationships between heights and the arm spans of students in Westminster Secondary School. We used a variety of different tools learned throughout this course to prove our hypothesis: The taller you are, the longer your arm span will be. Overall, we found that there's a strong positive correlation between the two data sets and that the higher the height, the longer the arm span.
There's been a lot of mystery and uncertainty about a persons height and if it affects the length of their arm span, so we decided to see if there was a relationship between height and arm span. More specifically, we conducted a survey to see if the taller a person stands, the longer their arm span will be.
Plan & Methodology
We took measurements of heights and arm spans of different students throughout Westminster, ranging from 14-19 years of age.
This is a type of sampling bias, we decided it was the best way to collect accurate data relating to our hypothesis.
It gives us an idea of how age groups effect the relationship between height and arm span.
We used a tape measure to measure the height from the bottom of the foot to the top of the head and to measure the arm span from the left middle finger to the right middle finger.
We experienced some difficulties when creating accurate measurements.
This could deliver some inaccurate results, but we still saw a relation between the two data sets
Histograms with Central Tendency
Correlation Between Two Data Sets
Strong positive correlation between these two data sets.
As the x variable increases (height), the y variable increases as well (arm span).
Normal Distribution Curve (Probability)
What is the probability that the next person we measure will have arm span and height of 180cm or higher?
The data of both sets is 61.76% being within the I.Q.R of heights, and 58.82% in the I.Q.R of arm span.
This tells us that the data is quite concentrated.
The left bound and right bound was calculated by adding and subtracting the standard deviation of both data sets respectively.
Free of outliers.
The box plot for heights has more condensed data.
The range of heights is the maximum value (194.5cm) minus the minimal value (153cm) giving us a range of 41.5 cm.
The range of armspan, is the maximum value (204cm) from the minimal value (149cm), giving a range of 55cm.
The I.Q.R. For arm span is 20 and the I.Q.R. For heights is 15.
Two viable options for a measure of central tendency.
Both are within the same number, but we will use the median for a central tendency.
Mean and Median of 173.735
Mode of 194
Most accurate measure of central tendency is both the mean and median
Both are identical, this represents a normal distribution.
Coefficient of Determination
A strong positive correlation of determination is present here, with a coefficient of determination of 0.977022, meaning that 97% of the variation for the y axis(arm span) is due to the variation of the x axis (heights).