Exercises

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 } & 80 \sim 89 & 90 \sim 99 & 100 \sim 109 \\ \hline f & 1 & 1 & 5 \end{array}

\begin{array}{c|cc} \text { Length } & 110 \sim 119 & 120 \sim 129 \\ \hline f & 2 & 1 \end{array}

\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.