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Interpreting Data, SM-Bank 017

Body mass index (BMI), in kilograms per square metre, was recorded for a sample of 32 men and displayed in the ordered stem plot below.
  

  1. Describe the shape of the distribution.  (1 mark)

  2. Determine the median BMI for this group of men.  (1 mark)

  3. People with a BMI of 25 or over are considered to be overweight.
  4. What percentage of these men would be considered to be overweight?  (1 mark)

Show Answers Only

a.    \(\text{Positively skewed}\)

b.    \(24.55\)

c.    \(37.5\%\)

Show Worked Solution

a.   \(\text{The tail is to the right, therefore positively skewed}\)
 

b.   \(32\ \text{data points}\)

\(\text{Median}\) \(=\dfrac{\text{(16th + 17th)}}{2}\)
  \(=\dfrac{ (24.5 + 24.6)}{2}\)
  \(= 24.55\)

 

c.    \(\text{Percentage}\) \(=\dfrac{12}{32}\times 100\)
    \(=37.5\%\)