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Is honey a cough remedy? Refer to the Archives of Pediatrics and Adolescent Medicine (December 2007) study of honey as a remedy for coughing. The coughing improvement scores (as determined by the children's parents) for the patients in the over-the-counter cough medicine dosage (DM) group, honey dosage group, and control group are reproduced in the accompanying table.

 Honey 12111511101310415169 Dosage: 141061081112128129111510159138121089512 DM Dosage: 46947779121011349127681212412137101394410159 No Dosage 5861081287716 (Control): 7712797951195688671094873143\begin{array}{lrrrrrrrrrrrrrr} \hline \text { Honey } & 12 & 11 & 15 & 11 & 10 & 13 & 10 & 4 & 15 & 16 & 9 & & \\ \text { Dosage: } & 14 & 10 & 6 & 10 & 8 & 11 & 12 & 12 & 8 & & & & \\ & 12 & 9 & 11 & 15 & 10 & 15 & 9 & 13 & 8 & 12 & 10 & & \\ & 8 & 9 & 5 & 12 & & & & & & & & \\ \hline \text { DM Dosage: } & 4 & 6 & 9 & 4 & 7 & 7 & 7 & 9 & 12 & 10 & 11 & & \\ & 3 & 4 & 9 & 12 & 7 & 6 & 8 & 12 & 12 & 4 & 12 & & \\ & 13 & 7 & 10 & 13 & 9 & 4 & 4 & 10 & 15 & 9 & & & \\ \hline \text { No Dosage } & 5 & 8 & 6 & 1 & 0 & 8 & 12 & 8 & 7 & 7 & 1 & 6 & \\ \text { (Control): } & 7 & 7 & 12 & 7 & 9 & 7 & 9 & 5 & 11 & 9 & 5 & & \\ & 6 & 8 & 8 & 6 & 7 & 10 & 9 & 4 & 8 & 7 & 3 & 1 & 4 & 3 \end{array}

Find the standard deviation of the improvement scores for the honey dosage group.

Question

For the stem-and-leaf plot below, what is the maximum and what is the minimum entry?

Key: 112=11.211|2=11.2.

Stem Leaf
1111 00 22
1212 44 66 66 77 88 99
1313 00 11 11 22 33 66 66 77 88 88
1414 33 44 66 66 88 99 99 99
1515 00 11 11 22 33 77 77 88 99
1616 22 22 55 77 88 88 99 99
1717 00 55

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To be able to answer this question, let us first explain what is the stem-and-leaf plot and how to read it. The stem-and-leaf plot is a representation of the data values in a table in which there are two main columns, one containing the first digit(s) and the other one containing last digit(s).

Depending on the given Key, we know how to read the data from the stem-and-leaf plot. For example, the Key: 112=11.211|2=11.2 indicates that the data set contains two-digit values with one decimal. So here, the stem column represents the predecimal value and the leaf represents the decimal value.

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