Question

a back-to-back stem-and-leaf plot compares two data sets by using the same stems for each data set. leaves for the first data set are on one side while leaves for the second data set are on the other side. the back-to-back stem-and-leaf plot available below shows the salaries (in thousands) of all lawyers at two small law firms. complete parts (a) and (b) below.

(a) what are the lowest and highest salaries at law firm a? at law firm b? how many lawyers are in each firm?

at law firm a the lowest salary was \\$ and the highest salary was \\$.
at law firm b the lowest salary was \\$ and the highest salary was \\$.

back-to-back stem-and-leaf plot
key: 5 | 19 | 0 = \\$195,000 for law firm a and \\$190,000 for law firm b

law firm a | | law firm b
6 0 | 9 | 0 2
8 5 2 2 2 | 10 | 5 7
9 9 6 1 1 | 11 | 1 1 4
2 2 | 12 | 0 3 3 5
| 13 | 2 2 5 9
| 14 | 0 3 3 3 9
| 15 | 4 4 4 5
| 16 | 3 9 9
9 9 5 1 0 | 17 | 1 2 5
5 5 5 2 1 | 18 | 9
9 9 8 7 4 | 19 | 5
4 | 20 |

Explanation:

Interpret the key and stems

The key is \(5 \mid 19 \mid 0 = \$195,000\) for Law Firm A and \(\$190,000\) for Law Firm B.
This means a stem of \(S\) and a leaf of \(L\) represents a salary of \(S \times 10 + L\) in thousands of dollars, which is \((10S + L) \times 1,000\).
For Law Firm A, the leaves are read from right to left (closest to the stem is the units digit, though they are listed in order).
For Law Firm B, the leaves are read from left to right.

Find the lowest and highest salaries for Law Firm A

• Lowest salary: The smallest stem with a leaf for Law Firm A is \(9\). The leaf is \(6\) (from the row \(6 \mid 9 \mid 0\)).

$$ \text{Salary} = 96 \times 1,000 = \$96,000 $$

• Highest salary: The largest stem with a leaf for Law Firm A is \(20\). The leaf is \(4\) (from the row \(4 \mid 20 \mid\)).

$$ \text{Salary} = 204 \times 1,000 = \$204,000 $$

Find the lowest and highest salaries for Law Firm B

• Lowest salary: The smallest stem with a leaf for Law Firm B is \(9\). The leaves are \(0, 2\). The smallest leaf is \(0\).

$$ \text{Salary} = 90 \times 1,000 = \$90,000 $$

• Highest salary: The largest stem with a leaf for Law Firm B is \(19\). The leaf is \(5\).

$$ \text{Salary} = 195 \times 1,000 = \$195,000 $$

Answer:

At Law Firm A the lowest salary was $96,000 and the highest salary was $<blank>204,000</blank>.
At Law Firm B the lowest salary was $90,000 and the highest salary was $<blank>195,000</blank>.