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Three Popular Data Displays

ANSWERS

  1. The vertical scale on one is the frequencies and on the other is the relative frequencies.

  1. \( \begin{array}{r|lllllll} 5 & 3 & & & & & \\ 6 & 8 & 9 & & & & \\ 7 & 0 & 0 & 0 & 5 & 6 & 7 & \\ 8 & 0 & 2 & 3 & 5 & 5 & 5 & 8 \\ 9 & 2 & 3 & 6 & & & \\ 10 & 0 & & & & & \end{array} \)

Frequency and relative frequency histograms are similarly generated.


  1. Noting that \(n=10\) the relative frequency table is:

\( \begin{array}{c|cccc} x & -1 & 0 & 1 & 2 \\ \hline f / n & 0.3 & 0.4 & 0.2 & 0.1 \end{array}\)

Since \(n\) is unknown, \(a\) is unknown, so the histogram cannot be constructed.

\( \begin{array}{r|l|llll} 8 & 7 & & & \\ 9 & 9 & & & \\ 10 & 0 & 5 & 5 & 7 & 8 \\ 11 & 8 & 9 & & & \\ 12 & 5 & & & \end{array}\)
Frequency and relative frequency histograms are similarly generated.

  1. \(\text { Noting } n=300 \text {, the relative frequency table is therefore: }\)

\( \begin{array}{c|cccc} \text { Blood Type } & O & A & B & A B \\ \hline f / n & 0.4533 & 0.4 & 0.1067 & 0.04 \end{array} \)

A relative frequency histogram is then generated.

The stem and leaf diagrams listed for Samples 1, 2, and 3 in that order.

  \(6\)  
  \(7\)  
  \(8\) \(7\)
  \(9\) \(9\)
  \(10\) \( 0 \quad 5 \quad 5 \quad 7 \quad 8\)
  \(11\) \( 8 \quad 9 \)
  \(12\) \(5\)
  \(13\)  
  \(14\)  
  \(15\)  
  \(16\)  
  \(6\)  
  \(7\)  
  \(8\)  
  \(9\)  
  \(10\)  
  \(11\)  
  \(12\)  
  \(13\) \(3\quad 7 \quad 8 \quad 8 \quad 9\)
  \(14\) \(0 \quad 2 \quad 5\)
  \(15\) \(2\)
  \(16\) \(0\)
\(6\) \(0\) \(9\)
\(7\) \(4\) \(4 \quad 9\)
\(8\) \(0\) \(0 \quad 2 \quad 2 \quad 2 \quad 2 \quad 3 \quad 3\)
\(9\)    
\(10\)    
\(11\)    
\(12\)    
\(13\)    
\(14\)    
\(15\)    
\(16\)    
The frequency tables are given below in the same order.

\( \begin{array}{c|ccc} \text { Length } & 130 \sim 139 & 140 \sim 149 & 150 \sim 159 \\ \hline f & 5 & 3 & 1 \end{array} \)

\( \begin{array}{c|c} \text { Length } & 160 \sim 169 \\ \hline f & 1 \end{array} \)

\( \begin{array}{c|ccc} \text { Length } & 60 \sim 69 & 70 \sim 79 & 80 \sim 89 \\ \hline f & 1 & 2 & 7 \end{array} \)

The relative frequency tables are given below in the same order.

\( \begin{array}{c|ccc} \text { Length } & 80 \sim 89 & 90 \sim 99 & 100 \sim 109 \\ \hline f / n & 0.1 & 0.1 & 0.5 \end{array}\)

\(\begin{array}{c|cc} \text { Length } & 110 \sim 119 & 120 \sim 129 \\ \hline f / n & 0.2 & 0.1 \end{array} \)

\( \begin{array}{c|ccc} \text { Length } & 130 \sim 139 & 140 \sim 149 & 150 \sim 159 \\ \hline f / n & 0.5 & 0.3 & 0.1 \end{array} \)

\( \begin{array}{c|c} \text { Length } & 160 \sim 169 \\ \hline f / n & 0.1 \end{array} \)

\( \begin{array}{c|ccc} \text { Length } & 60 \sim 69 & 70 \sim 79 & 80 \sim 89 \\ \hline f / n & 0.1 & 0.2 & 0.7 \end{array} \)

    1. \(19\).
    2. \(20\).