Question

1. a survey of 20 patients was done at a local hospital. the number of pills each patient was given per day was recorded as follows.

10 6 8 15
2 7 14 10
12 8 11 9
1 7 9 5
13 15 3 6
(a) construct a stem-and-leaf display for these data.
(b) what conclusions can you draw from the graph?

Explanation:

Part (a)

Step1: Identify stems (tens place)

Stems are the tens digit of each number. Possible stems: 0, 1 (since numbers range from 1 to 15).

Step2: List leaves (units place) for each stem

• Stem 0 (numbers 1,2,3,5,6,6,7,7,8,8,9,9): Leaves: 1,2,3,5,6,6,7,7,8,8,9,9
• Stem 1 (numbers 10,10,11,12,13,14,15,15): Leaves: 0,0,1,2,3,4,5,5

Step3: Construct stem - and - leaf display

Stem	Leaf
1	0, 0, 1, 2, 3, 4, 5, 5

Part (b)

1. Distribution Shape: The data seems to be somewhat symmetric around the middle values. For stem 0, the leaves are spread from 1 - 9 and for stem 1, from 0 - 5. There is no extreme skewness (no long tail on one side).
2. Frequency of Values: Values in the lower range (0 - 9 pills) are more frequent (12 values) compared to the higher range (10 - 15 pills, 8 values). The values 6,7,8,9,0 (for stem 1) and 5,6 (for stem 0) have relatively higher frequencies (appearing twice or more).
3. Range: The range of the number of pills per day is from 1 to 15 (since the minimum value is 1 and maximum is 15).

Answer:

s:
(a)

Stem	Leaf
1	0, 0, 1, 2, 3, 4, 5, 5

(b) The data has a relatively symmetric distribution (no extreme skewness), most values are in the 0 - 9 (tens place 0) range, with a range of 1 to 15 pills per day. Frequent values include 6,7,8,9,0 (for stem 1), 5,6 (for stem 0).