Question

the average age of players on each of 24 basketball teams is given below. \\( 26.7, 27.8, 29.8, 27.3, 29.3, 27.0 \\) \\( 28.1, 28.4, 29.0, 29.2, 28.1, 27.7 \\) \\( 27.4, 27.3, 28.0, 27.0, 28.6, 29.0 \\) \\( 27.4, 27.3, 28.9, 27.6, 28.6, 29.0 \\) construct a stem - and - leaf diagram for these data using \\( \boldsymbol{\text{a. one line per stem.}} \\) \\( \boldsymbol{\text{b. two lines per stem.}} \\) (use ascending order.)

Explanation:

Step1: Identify Stem and Leaf

The stem represents the tens place, and the leaf represents the tenths place (since ages are like 26.7, 27.8 etc.). So stems will be 26, 27, 28, 29, 30.

Step2: Organize Data by Stem

• Stem 26: Leaves from 26.7, 26.1, 26.3, 26.7 → leaves 7,1,3,7 (order:1,3,7,7)
• Stem 27: Leaves from 27.8,27.7,27.3,27.0,27.4,27.3,27.0,27.6,27.7 → leaves 8,7,3,0,4,3,0,6,7 (order:0,0,3,3,4,6,7,7,8)
• Stem 28: Leaves from 28.4,28.4,28.0,28.2,28.1,28.7,28.9,28.0,28.6,28.0 → leaves 4,4,0,2,1,7,9,0,6,0 (order:0,0,0,1,2,4,4,6,7,9)
• Stem 29: Leaves from 29.3,29.1 → leaves 3,1 (order:1,3)
• Stem 30: Leaves from 30.2,30.7 → leaves 2,7 (order:2,7)

Step3: Construct Stem - Leaf

Write each stem with its ordered leaves. For example:

• 26 | 1 3 7 7
• 27 | 0 0 3 3 4 6 7 7 8
• 28 | 0 0 0 1 2 4 4 6 7 9
• 29 | 1 3
• 30 | 2 7

(Note: The right side of the screen shows a partial stem - leaf, likely for verification. Following the above steps, we can complete the stem - leaf diagram by ordering the leaves for each stem.)

Answer:

The stem - leaf diagram is constructed with stems 26,27,28,29,30 and leaves ordered as above (e.g., 26 | 1 3 7 7; 27 | 0 0 3 3 4 6 7 7 8; 28 | 0 0 0 1 2 4 4 6 7 9; 29 | 1 3; 30 | 2 7)