91Ó°ÊÓ

Refer to Table \(15-13,\) which gives the home-to-school distance \(d\) (rounded to the nearest half-mile) for each of the 27 kindergarten students at Cleansburg Elementary School. $$ \begin{array}{c|c|c|c} \begin{array}{c} \text { Student } \\ \text { ID } \end{array} & \boldsymbol{d} & \begin{array}{c} \text { Student } \\ \text { ID } \end{array} & \boldsymbol{d} \\ \hline 1362 & 1.5 & 3921 & 5.0 \\ \hline 1486 & 2.0 & 4355 & 1.0 \\ \hline 1587 & 1.0 & 4454 & 1.5 \\ \hline 1877 & 0.0 & 4561 & 1.5 \\ \hline 1932 & 1.5 & 5482 & 2.5 \\ \hline 1946 & 0.0 & 5533 & 1.5 \\ \hline 2103 & 2.5 & 5717 & 8.5 \\ \hline 2877 & 1.0 & 6307 & 1.5 \\ \hline 2964 & 0.5 & 6573 & 0.5 \\ \hline 3491 & 0.0 & 8436 & 3.0 \\ \hline 3588 & 0.5 & 8592 & 0.0 \\ \hline 3711 & 1.5 & 8964 & 2.0 \\ \hline 3780 & 2.0 & 9205 & 0.5 \\ \hline & & 9658 & 6.0 \\ \hline \end{array} $$ (a) Make a frequency table for the distances in Table \(15-13 .\) (b) Draw a line graph for the data in Table \(15-13\).

Refer to Table \(15-13,\) which gives the home-to-school distance \(d\) (rounded to the nearest half-mile) for each of the 27 kindergarten students at Cleansburg Elementary School. $$ \begin{array}{c|c|c|c} \begin{array}{c} \text { Student } \\ \text { ID } \end{array} & \boldsymbol{d} & \begin{array}{c} \text { Student } \\ \text { ID } \end{array} & \boldsymbol{d} \\ \hline 1362 & 1.5 & 3921 & 5.0 \\ \hline 1486 & 2.0 & 4355 & 1.0 \\ \hline 1587 & 1.0 & 4454 & 1.5 \\ \hline 1877 & 0.0 & 4561 & 1.5 \\ \hline 1932 & 1.5 & 5482 & 2.5 \\ \hline 1946 & 0.0 & 5533 & 1.5 \\ \hline 2103 & 2.5 & 5717 & 8.5 \\ \hline 2877 & 1.0 & 6307 & 1.5 \\ \hline 2964 & 0.5 & 6573 & 0.5 \\ \hline 3491 & 0.0 & 8436 & 3.0 \\ \hline 3588 & 0.5 & 8592 & 0.0 \\ \hline 3711 & 1.5 & 8964 & 2.0 \\ \hline 3780 & 2.0 & 9205 & 0.5 \\ \hline & & 9658 & 6.0 \\ \hline \end{array} $$ Draw a bar graph for the data in Table \(15-13\).

Table \(15-20\) shows the ages of the firefighters in the Cleansburg Fire Department. $$ \begin{array}{l|c|c|c|c|c} \text { Age } & 25 & 27 & 28 & 29 & 30 \\ \hline \text { Frequency } & 2 & 7 & 6 & 9 & 15 \\ \hline \text { Age } & 31 & 32 & 33 & 37 & 39 \\ \hline \text { Frequency } & 12 & 9 & 9 & 6 & 4 \\ \hline \end{array} $$ (a) Find the average age of the Cleansburg firefighters rounded to two decimal places. (b) Find the median age of the Cleansburg firefighters.

Table \(15-21\) shows the relative frequencies of the scores of a group of students on a philosophy quiz. $$ \begin{array}{l|c|c|c|c|c} \text { Score } & 4 & 5 & 6 & 7 & 8 \\ \hline \begin{array}{l} \text { Relative } \\ \text { frequency } \end{array} & 7 \% & 11 \% & 19 \% & 24 \% & 39 \% \end{array} $$ (a) Find the average quiz score. (b) Find the median quiz score.

Table \(15-22\) shows the relative frequencies of the scores of a group of students on a 10 -point math quiz. $$ \begin{array}{l|c|c|c|c|c|c|c} \text { Score } & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline \begin{array}{l} \text { Relative } \\ \text { frequency } \end{array} & 8 \% & 12 \% & 16 \% & 20 \% & 18 \% & 14 \% & 12 \% \end{array} $$ (a) Find the average quiz score rounded to two decimal places. (b) Find the median quiz score.

The purpose is to practice computing standard deviations the old fashioned way (by hand). Granted, computing standard deviations this way is not the way it is generally done in practice; a good calculator (or a computer package) will do it much faster and more accurately. The point is that computing a few standard deviations the old-fashioned way should help you understand the concept a little better. If you use a calculator or a computer to answer these exercises, you are defeating their purpose. Find the standard deviation of each of the following data sets. (a) \\{3,3,3,3\\} (b) \\{0,6,6,8\\} (c) \\{-6,0,0,18\\} (d) \\{6,7,8,9,10\\}

Refer to histograms with unequal class intervals. When sketching such histograms, the columns must be drawn so that the frequencies or percentages are proportional to the area of the column. Figure \(15-21\) illustrates this. If the column over class interval 1 represents \(10 \%\) of the population, then the column over class interval 2 , also representing \(10 \%\) of the population, must be one-third as high, because the class interval is three times as large (Fig. \(15-21\) ). Two hundred senior citizens are tested for fitness and rated on their times on a one-mile walk. These ratings and associated frequencies are given in Table 15-23. Draw a histogram for these data based on the categories defined by the ratings in the table. $$ \begin{array}{l|c|c} \text { Time } & \text { Rating } & \text { Frequency } \\ \hline 6^{+} \text {to } 10 \text { minutes } & \text { Fast } & 10 \\ \hline 10^{+} \text {to } 16 \text { minutes } & \text { Fit } & 90 \\ \hline 16^{+} \text {to } 24 \text { minutes } & \text { Average } & 80 \\ \hline 24^{+} \text {to } 40 \text { minutes } & \text { Slow } & 20 \end{array} $$