By: Thomas B Block: 5 Pre-Calculus (grade 10) Ms. Nazan IB Math Statistics Project
The Relationship of Weight and Height in Adult Males
Task: Obtain a sample of the height and weight of 20 males above the age of 18 and analyze the collected data in order to find a possible correlation between these two variables.
Plan: Interview people during breakfast at Slaveiro Hotel in the city of Sao Paulo. Then organize the collected data into a scatter plot, two histograms and two box-and-whisker diagrams, and draw conclusions from them.
In order to find intervals for height, the formula 1+3.3*log(n) was used. It yielded the result 5.2, which rounds up to six intervals. This in turn yields an interval width of 5. In order to simplify data analysis, the same interval width was used for both weight and height. Thus, weight has 9 intervals.
Class Intervals – Height (cm) Interval Frequency 165-169 3 170-174 3 175-179 11 180-184 2 185-189 0 190-194 1
Scatter Plot Analysis
As evidenced by the scatter plot and regression line on the previous slide, weight and height in males over the age of 18 (matured growth cycle) are strongly correlated. The higher height, the larger the weight (but not necessarily vice-versa).
Another piece of information provided by this plot is that height and weight are clustured in the 60-65kg range and the 170-175cm range respectively.
Histogram - Weight
Analysis of Weight Histogram
Although this distribution presents a shape of a pseudo-normal distribution, it is skewed, as a large part of the sample had a weight between 70-74 kilograms.
Most of the sample has a weight in between 55-72 kg, disregarding the 62-65 kg and the 72-77 kg intervals.
Data is most densely concentrated (70%) within one standard deviation of the mean, following the rule of a normal distribution. However, since a histogram is a visual representation of data, this claim is refutable.
Box-and-Whisker Diagram - Weight
Analysis of Weight Box-and-Whisker Diagram
An important thing to note about box-and-whisker diagrams is that they disregard the statistical distribution of a sample. The spaces in between the boxes and whiskers of this diagram show the dispersion of data.
The most dispersion in this weight sample is found in the upper quartile, such that data one standard deviation away from the mean is majoritarily placed in the upper quartile.
Thus, weights below 72 kg (median) vary much less than weight above 72 kg in adult males over the age of 18.
Histogram - Height
Analysis of Height Histogram
The shape of this data shows that height is skewed in the 172-175cm range. In fact, 11 out of 20 male adults have heights in this range.
Data is most densely concentrated within one to the left of the mean, more specifically about one standard deviation below it.
More than 50% of the data lies one standard deviation below the mean. Shorter adult males are more common than taller adult males in this sample.
Box-and-Whisker Diagram - Height
Analysis of Height Box-and-Whisker Diagram
Data in the nonexistent upper quartile in this diagram supposedly presents vary little variation, with the exception of outliers such as the height of 190 cm.
Since the upper quartile is found in the same place as the mean, data is completely clustered roughly one standard deviation below the mean.
This shows (again) that there are more adult men below the average height than above it.
Height and weight among adult males are strongly correlated. Although most adult males heights' lie within one standard deviation below the mean, most adult males weights' lie one standard deviation above the mean. Adult heights are more skewed and not nearly as dispersed as adult weights within this sample.
The analysis of the data found in this sample of twenty male adults indicates that weight is directly correlated with height.
Validity – Analysis of Data
Even though the analysis indicates that the height and weight of male adults are directly correlated, more weight does not necessarily mean more height, yet more height generally means more weight. More height means larger bones, which in turn leads to more weight. More weight may also mean larger bones (more height), but it can also mean more body fat, which does not mean more height.
Validity – Data Collection
The data collected in the sample presented was collected through interviews. Interviews about people's physical aspects are not a very reliable way of obtaining information.
People can lie about their height and weight, or simply not know it precisely.
Having a measuring tape and a scale to measure these physical aspects is a far more reliable way of collecting information, though it is more time consuming and harder to do (people may be reluctant to get measured).
"Box Plot: Display of Distribution." Tools for Science. Web. 14 Mar. 2011. <http://www.physics.csbsju.edu/stats/box2.html>.
"Class Interval." Build Your Own Broadband and Phone Package with TalkTalk. Web. 14 Mar. 2011. <http://www.talktalk.co.uk/reference/encyclopaedia/hutchinson/m0026012.html>.
"Frequency Distributions." IRI/LDEO Climate Data Library. Web. 14 Mar. 2011. <http://iridl.ldeo.columbia.edu/dochelp/StatTutorial/Frequency/>.