Question

The numbers below are the mean distances from the sun (in millions of miles) of the first ten asteroids. Use a stem-and-leaf plot to order the distances from least to greatest. (Hint: Use \(25 | 70=257.0\) for your key.) $$257.0,257.4,247.8,219.3,239.3,225.2,221.4,204.4,221.7,222.6$$

Short answer

Stem-and-leaf plot: \n 20 | 44 \n 21 | 937 4 \n 22 | 567 \n 23 | 78 \n 24 | 78 \n 25 | 70 74 \n This indicates the ordered numbers as: 204.4, 219.3, 213.7, 221.4, 225.2, 257.0, 257.4.

Step-by-step solution

Understand the Stem-and-Leaf Key

The key for a stem-and-leaf plot consists of a stem and leaf. In the key given, \(25 | 70\), the number to the left of the vertical line (\(25\)) is the stem, and the number to the right (\(70\)) is the leaf. This key indicates that the tens and hundreds places are part of the stem and the ones and decimal places are considered to be the leaf.

Construct the stem-and-leaf plot

To construct a stem-and-leaf plot with the given data, identify the stems and leaves from each data point using the key and order them from least to greatest. Hence, the plot will look like \n 20 | 44 \n 21 | 937 4 \n 22 | 567 \n 23 | 78 \n 24 | 78 \n 25 | 70 74.

Interpret the stem-and-leaf plot

Each entry in the plot should be read using the key. For example, the row '20 | 44' indicates the two numbers 204.4. Similarly for the row '21 | 937 4', it indicates the numbers 219.3, 213.7 and 221.4. Done in such a manner, all numbers can be organized and presented following the ascending order.