Questions: The data represents the heights of eruptions by a geyser. Use the heights to construct a stemplot. Identify the two values that are closest to the middle when the data are sorted in order from lowest to highest. Height of eruption (in.): 60, 36, 50, 90, 80, 50, 40, 70, 50, 64, 73, 57, 51, 65, 66, 60, 77, 70, 41, 88 Which plot represents a stemplot of the data? A. 3 6 4 01 5 00017 6 00456 7 0037 8 08 9 0 B. 3 0 11 4 0 07 5 0 04 6 0 06 7 0 05 8 037 9 08 C. 3 6 4 0004567 5 00037 6 008 7 0011 8 0 9 0

Solution Steps

To solve this problem, we need to:

1. Sort the given data in ascending order.
2. Identify the two middle values in the sorted list.
3. Construct a stemplot from the sorted data.
4. Compare the constructed stemplot with the given options to identify the correct one.

The given data is: \[ \{60, 36, 50, 900, 80, 50, 40, 70, 50, 64, 73, 57, 51, 65, 66, 60, 77, 70, 41, 88\} \]

Sorting the data in ascending order, we get: \[ \{36, 40, 41, 50, 50, 50, 51, 57, 60, 60, 64, 65, 66, 70, 70, 73, 77, 80, 88, 900\} \]

The number of data points \( n = 20 \). The two middle values are: \[ \text{middle1} = \text{sorted\_data}\left(\frac{n}{2} - 1\right) = 60 \] \[ \text{middle2} = \text{sorted\_data}\left(\frac{n}{2}\right) = 64 \]

To construct the stemplot, we separate each number into a stem (the leading digit(s)) and a leaf (the trailing digit). The stemplot is:

\[ \begin{array}{l|l} 3 & 6 \\ 4 & 01 \\ 5 & 00017 \\ 6 & 00456 \\ 7 & 0037 \\ 8 & 08 \\ 90 & 0 \\ \end{array} \]

Comparing the constructed stemplot with the given options, we find that option A matches our stemplot.

Final Answer