A Wide Variety of Oak Trees Grow in the United $m ^ { 3 }$

Essay

A wide variety of oak trees grow in the United States. In one
Acorn Statistics study, a sample of acorns was collected from different locations, and their volumes, in $m ^ { 3 }$ , were recorded. The table at right presents summary statistics for these data.
$\begin{array}{l}\text { Acorn Statistics }\\\begin{array} { | l | c | } \hline \text { Statistic } & \text { Value } \\\hline \mathrm { N } & 38 \\\text { Mean } & 3.0 \\\text { Median } & 1.8 \\\text { St. Dev. } & 2.6 \\\text { Minimum } & 0.3 \\\text { Maximum } & 10.5 \\\text { 1st Quartile } & 1.1 \\\text { 3rd Quartile } & 4.3 \\\hline\end{array}\end{array}$

(a) Describe a procedure that uses some or all of these summary statistics to determine whether outliers are present in the data.

(b) Using your procedure from part (a), determine if there are outliers in these data. 3 Engineers initially surveyed the Territory of Iowa in the 1830 's, and they were very careful to take note of the trees and vegetation. The sample of hickory tree diameters from the original survey of what is now Linn County, is presented in the stem and leaf plot below. The display uses five lines for each stem. Thus, "1t|" is the stem for diameters of 12 and 13 , "1f|" for 14 and 15 , "1s|" for 16 and 17, and so on. (The "t" then stands for leaves that are twos and threes, the " $\mathrm { f }$ " for leaves of fours and fives, etc.)

The mean diameter of the 73 hickory trees in this sample is $11.849$ inches, and the standard deviation is $3.995$ inches.
Linn County Trees in 1830
Hickory Diameters
$\begin{aligned} 1 \mid 0 = 10 & \text { inches } \quad N = 73 \\ & 0 . \mid \\ & 0 t \mid \\ & 0 f \mid 45 \\ & 0 s \mid 666666677 \\ & 0 * \mid 88888888999 \\ & 1 . \mid 00000000 \\ & 1 t \mid 222222222222222 \\ & 1 f \mid 4444444444445 \\ & 1 \mathrm {~s} \mid 666 \\ & 1 * \mid 88888888888 \\ & 2 . \mid 0 \\ & 2 \mathrm { t } \mid \\ & 2 \mathrm { fl } \\ & 2 \mathrm {~s} \mid \\ & 2 * \mid \end{aligned}$
(a) What is the approximate diameter of a hickory tree at the 20th percentile in this
distribution?
(b) According to the Empirical Rule, approximately 68% of hickory tree diameters
are between what two values?