Question

the data represents the heights of eruptions by a geyser. height of eruption (in.) 68 80 50 57 70 33 50 40 72 66 42 90 70 53 60 80 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. which plot represents a stemplot of the data? a. 3|3 4|02 5|00237 6|68 7|00 8|00 9|0 b. 3|3 4|02 5|0037 6|01668 7|00 8|00 9|0 c. 3|027 4|068 5|0006 6|001 7|00 8|00 9|0

Explanation:

Step1: Sort the data

33, 40, 42, 50, 50, 53, 57, 60, 61, 66, 66, 70, 70, 70, 72, 80, 80, 90

Step2: Determine the median - related values

There are 18 data - points. The median position is $\frac{18 + 1}{2}=9.5$. So the two values closest to the middle are the 9th and 10th values when sorted. The 9th value is 61 and the 10th value is 66.

Step3: Construct the stem - plot

The stems are the tens digits and the leaves are the units digits.
Stem | Leaf
--- | ---
3 | 3
4 | 0 2
5 | 0 0 3 7
6 | 0 1 6 6
7 | 0 0 0 2
8 | 0 0
9 | 0

Comparing with the given options, we can see that the correct stem - plot is the one that matches our constructed one.

Answer:

(The stem - plot is not fully shown in the options here in a way that we can directly pick an option letter, but the two values closest to the middle are 61 and 66)