Introduction

What is BMI?

The Body Mass Index (BMI) is a measurement tool used to classify a range of health risk categories. It is a statistical measure of body weight based on a person's weight and height. The formula to calculate a person’s BMI is by taking the weight in kilograms dividing by the square of the person’s height in metres:

(Picture adopted from Know Your BMI, Health Promotion Board: http://www.knowyourbmi.sg/knowyourrisks.aspx)

 

Although BMI does not measure body fat directly, research has shown that BMI correlates to direct measures of body fat. A BMI of 23 or more puts you at greater risk of obesity-related diseases. Hence, knowing your BMI is crucial to battling obesity as it can help you assess the health risks you are exposed to and take preventive steps to better manage your weight.
Below is a graph showing the level of risk corresponding to BMI value:

(Picture adopted from Know Your BMI, Health Promotion Board: http://www.knowyourbmi.sg/knowyourrisks.aspx)

Importance of Study

BMI is dependent only upon weight and height and it makes simplistic assumptions about the distribution of muscle and bone mass. Due to its straightforward measurement and calculation, it is the most widely used diagnostic tool to identify weight problem within a population (underweight, overweight, obesity).

Based on the formula stated above, we can see that for a given height, BMI is directly proportional to weight. For instance, if body weight increases by 50%, BMI will also increase by approximately 50% :

Given weight= 50kg and height= 1.6m,

BMI = 50/(1.6 x 1.6) = 19.5

Should weight increases by 50% ( 50kg to 75kg) and height remains the same,

BMI = 75/(1.6 x 1.6) = 29.3

 

On the other hand, for a given weight, BMI is inversely proportional to the square of height. For instance, if height increases by 10%, BMI will decrease by approximately 20% :

Given weight= 50kg and height= 1.6m

BMI = 50/(1.6 x 1.6) = 19.5

Should height increases by 10% (1.6m to 1.76m) and weight remains,

BMI = 50/(1.76 x 1.76) = 16.1

However, in real life, the above situation is largely unrealistic as an increase in height would often be accompanied by a corresponding increase in body and bone mass, resulting in an increase in weight. As such, we would like to investigate if BMI does have any significant relation to height.

 

Selected Variables

Since we are finding the relationship between one's BMI and height, our chosen variables are

1. Body Mass Index (BMI)

2. Height (in metres)

Both variables are ratio-scale variables which have a true zero point and constant intervals. As height is needed to calculate the BMI, it is seen as the independent variable while BMI is the dependent.

Hypothesis

Null hypothesis: There is no relation in a person’s BMI to his height.

Hypothesis: There is a relation in a person’s BMI to his height.