Three Popular Data Displays

This section elaborates on how to describe data. In particular, you will learn about the relative frequency histogram. Complete the exercises and check your answers.

EXERCISES

BASIC

  1. Describe one difference between a frequency histogram and a relative frequency histogram.

  1. Construct a stem and leaf diagram, a frequency histogram, and a relative frequency histogram for the following data set. For the histograms use classes 51–60, 61–70, and so on.

\begin{array}{lllll} 69 & 92 & 68 & 77 & 80 \\ 70 & 85 & 88 & 85 & 96 \end{array}

 

\begin{array}{lllll}93 & 75 & 76 & 82 & 100 \\ 53 & 70 & 70 & 82 & 85\end{array}

  1. A data set contains n = 10 observations. The values x and their frequencies f are summarized in the following data frequency table.

 \begin{array}{c|cccc} x & -1 & 0 & 1 & 2 \\ \hline f & 3 & 4 & 2 & 1 \end{array} 

  1. A data set has the following frequency distribution table:

     \begin{array}{l|llll} x & 1 & 2 & 3 & 4 \\ \hline f & 3 & a & 2 & 1 \end{array} 

    The number a is unknown. Can you construct a frequency histogram? If so, construct it. If not, say why not.

 

APPLICATIONS

  1. The IQ scores of ten students randomly selected from an elementary school are given.

    \begin{array}{ccccc}108 & 100 & 99 & 125 & 87 \\ 105 & 107 & 105 & 119 & 118\end{array}

    Grouping the measures in the 80s, the 90s, and so on, construct a stem and leaf diagram, a frequency histogram, and a relative frequency histogram.

  1. During a one-day blood drive 300 people donated blood at a mobile donation center. The blood types of these 300 donors are summarized in the table.

     \begin{array}{c|cccc} \text { Blood Type } & O & A & B & A B \\ \hline \text { Frequency } & 136 & 120 & 32 & 12 \end{array} 

    Construct a relative frequency histogram for the data set.

 

ADDITIONAL EXERCISES

  1. Random samples, each of size n = 10, were taken of the lengths in centimeters of three kinds of commercial fish, with the following results:

     \begin{array}{rrrrrr} \text { Sample 1: } & 108 & 100 & 99 & 125 & 87 \\ & 105 & 107 & 105 & 119 & 118 \\ \text { Sample 2: } & 133 & 140 & 152 & 142 & 137 \\ & 145 & 160 & 138 & 139 & 138 \\ \text { Sample 3: } & 82 & 60 & 83 & 82 & 82 \\ & 74 & 79 & 82 & 80 & 80 \end{array} 

    Grouping the measures by their common hundreds and tens digits, construct a stem and leaf diagram, a frequency histogram, and a relative frequency histogram for each of the samples. Compare the histograms and describe any patterns they exhibit.

  1. In a particular kitchen appliance store, the weekly sales of an electric automatic rice cooker for the last 20 weeks are as follows.

\begin{array}{lllll}20 & 15 & 14 & 14 & 18 \\ 15 & 17 & 16 & 16 & 18\end{array}

 

\begin{array}{ccccc}15 & 19 & 12 & 13 & 9 \\ 19 & 15 & 15 & 16 & 15\end{array}

In retail sales, too large an inventory ties up capital, while too small an inventory costs lost sales and customer satisfaction. Using the relative frequency histogram for these data, find approximately how many rice cookers must be in stock at the beginning of each week if

    1. the store is not to run out of stock by the end of a week for more than 15% of the weeks; and
    2. the store is not to run out of stock by the end of a week for more than 5% of the weeks.