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Data Analysis, SM-Bank 046

The back-to-back ordered stem-and-leaf plot below shows the female and male smoking rates, expressed as a percentage, in 18 countries.
 

  1. For the 18 countries listed, what is the range of the male smoking rates?  (1 mark)
  2. For the 18 countries listed, what is the mode of the female smoking rates?  (1 mark)
  3. For the 18 countries listed, what is the difference between the medians of the female and male smoking rates?  (2 marks)
Show Answers Only

a.     \(30\%\)

b.     \(25\%\)

c.     \(5.5\%\)

Show Worked Solution

a.    \(\text{Range}=47-17=30\%\)

b.    \(\text{Female mode}=25\%\)

c.     \(\text{Female Median }\) \(=\ \text{average of 9th and 10th scores}\)
    \(=\dfrac{21+22}{2}=21.5\%\)

 

\(\text{Male Median }\) \(=\ \text{average of 9th and 10th scores}\)
  \(=27\%\)

  
\(\therefore\ \text{The difference in medians}\)

\(=27-21.5=5.5\%\)