A group of students were asked to guess the width of the room in feet, measured to the nearest foot (1 meter = 3.28 feet, to 2 decimal places). Construct a back to back stemplot from these two datasets. How will you overcome the problem that different units are used in the two datasets?
Guesses (Meters)
8 9 10 10 10 10 10 10 11 11 11 11 12
Guesses (Feet)
24 25 27 30 30 30 30 30 30 32 32 33 34
To construct a back-to-back stem plot from the two datasets, we need to convert the values in one dataset to the same units as the other dataset. In this case, we'll convert the guesses in meters to feet to match the units used in the guesses in feet dataset.
To convert the values from meters to feet, we can multiply each value by the conversion factor, which is 3.28 since 1 meter is equal to 3.28 feet. We'll round the converted values to two decimal places to match the precision of the original data.
Here's how we can convert the values from meters to feet:
Guesses (Meters):
8 9 10 10 10 10 10 10 11 11 11 11 12
- Multiply each value by 3.28:
24.64 29.52 32.80 32.80 32.80 32.80 32.80 32.80 36.08 36.08 36.08 36.08 39.36
Now that we have the converted values in feet, we can construct the back-to-back stem plot. Here's how it can be done:
Back-to-Back Stem Plot:
G (M): 8 9 10 10 10 10 10 10 11 11 11 11 12
|
F (F): | 2 4 5 7 0 0 0 0 0 2 2 3 4
G (M): | 8 9 0 0 0 0 0 0 1 1 1 1 2
Explanation:
- On the left side, we have the "G (M)" stem representing the guesses in meters.
- On the right side, we have the "G (M)" stem representing the converted guesses in feet.
- The "F (F)" stem represents the guesses in feet.
- The numbers on the left side of the stem represent the tens digit of the values, while the numbers on the right side represent the ones digit.
- The lines connecting the matching values ("10" in this case) show a back-to-back stem plot.
Note: The stem plot is constructed in a way that allows easy comparison between the two datasets while also accommodating different units.