Question

63, 51, 55, 55, 66, 71, 87, 95, 81, 68, 55, 52, 65, 54, 50, 66, 59, 66, 71, 72
a) data were collected for 1 qualitative variable(s).
is it appropriate to make a stem - and - leaf plot for this type of data and number of variables? yes.
b) complete the stem - and - leaf plot below.
you must put commas between the leaves.
stems leaves
5 0,0,1,2,4,5,5,5,8,9,9
empty stem rows follow

Explanation:

Part b) Completing the Stem - and - Leaf Plot

First, we list out all the data points: 63, 51, 55, 55, 66, 71, 87, 95, 81, 68, 55, 52, 65, 54, 50, 66, 59, 66, 71, 72. We already have the stem 5 with leaves 0,0,1,2,4,5,5,5,8,9,9 (corresponding to numbers in the 50s: 50, 50, 51, 52, 54, 55, 55, 55, 58, 59, 59? Wait, actually, let's re - extract the numbers in each ten - s place:

• Stem 6: The numbers in the 60s are 63, 66, 68, 65, 66, 66. So the leaves (the units digits) are 3, 6, 8, 5, 6, 6. We sort them: 3,5,6,6,6,8.
• Stem 7: The numbers in the 70s are 71, 71, 72. The leaves (units digits) are 1,1,2. We sort them: 1,1,2.
• Stem 8: The numbers in the 80s are 87, 81. The leaves (units digits) are 7,1. We sort them: 1,7.
• Stem 9: The number in the 90s is 95. The leaf (units digit) is 5.

Step 1: Stem 6

Identify numbers with tens digit 6
The numbers are 63, 65, 66, 66, 66, 68. The units digits (leaves) are 3, 5, 6, 6, 6, 8. Sorting them gives 3, 5, 6, 6, 6, 8.

Expression: Stem = 6, Leaves = 3,5,6,6,6,8

Step 2: Stem 7

Identify numbers with tens digit 7
The numbers are 71, 71, 72. The units digits (leaves) are 1, 1, 2. Sorting them gives 1, 1, 2.

Expression: Stem = 7, Leaves = 1,1,2

Step 3: Stem 8

Identify numbers with tens digit 8
The numbers are 81, 87. The units digits (leaves) are 1, 7. Sorting them gives 1, 7.

Expression: Stem = 8, Leaves = 1,7

Step 4: Stem 9

Answer:

• Stem 6: Leaves = 3,5,6,6,6,8
• Stem 7: Leaves = 1,1,2
• Stem 8: Leaves = 1,7
• Stem 9: Leaves = 5

So the completed stem - and - leaf plot rows (after stem 5) are:

Stems	Leaves
7	1,1,2
8	1,7
9	5