Question

a random sample of 40 college professors is selected from all professors at a university. the following list gives their ages.
66, 48, 46, 42, 30, 51, 47, 44, 48, 21, 58, 62, 56, 44, 61,
68, 59, 49, 51, 28, 37, 68, 41, 45, 32, 39, 40, 31, 27, 44,
69, 31, 36, 41, 23, 34, 45, 33, 36, 54.
construct a stem - and - leaf plot for the data. complete parts a. and b.
a. determine the leaves for each corresponding stem. complete the table below.
(use ascending order.)
\

$$\begin{tabular}{c|c} stem & leaves \\\\ hline 2 & 1,3,7,8 \\\\ 3 & \\square \\\\ \\end{tabular}$$

Explanation:

Step1: Identify data with stem 3

Look for numbers in the data set where the tens - digit is 3. The numbers are 30, 37, 32, 39, 31, 36, 34, 33, 36.

Step2: Extract the units - digit (leaves)

For 30, the leaf is 0; for 37, the leaf is 7; for 32, the leaf is 2; for 39, the leaf is 9; for 31, the leaf is 1; for 36, the leaf is 6; for 34, the leaf is 4; for 33, the leaf is 3; for 36, the leaf is 6.

Step3: Sort the leaves

Sort the leaves \(0,7,2,9,1,6,4,3,6\) in ascending order. Using the rule of comparing single - digit numbers (\(0<1<2<3<4<6 = 6<7<9\)), we get \(0,1,2,3,4,6,6,7,9\)

Answer:

\(0,1,2,3,4,6,6,7,9\)