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# stem – and – leaf display

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```Exercise 3.1
Objective:
To find summary numbers and construct a letter value display for a given batch of data/observations and describe it based on the display.
Task: Answer individually or by pair the problems in this exercise. Do as indicated. Tools and Resources: Course handout and other
supplementary resource materials.
Procedure:
1) Use the appropriate definition and suitable variation of a stem – and – leaf display for the given batch of data below.
2) Show all necessary computations in your answer sheet. Answer the items in chronological order.
3) Be ready with your solutions during the scheduled synchronous session.
4) You are encouraged to discuss with your classmates.
Problem
Consider the following batch of observations.
50.7
53.0
54.1
55.7
64.3
69.5
71.4
74.4
82.5
85.8
51.5
53.4
55.3
59.5
67.3
70.2
72.3
77.8
82.7
87.5
52.4
53.5
55.7
63.5
69.1
70.5
73.0
78.5
84.3
95.4
1) Give the depths of the observations.
2) Determine the 7 – letter values and their corresponding depths.
3) Construct the corresponding 7 – letter value display. Make sure to show the “mids” and “spread”.
4) Determine the shape and spread of the batch.
5) Provide the cut-offs and check if there are outliers.
n = 30
Data 50.7 51.5 52.4 53.0 53.4 53.5 54.1 55.3 55.7 55.7 59.5 63.5 64.3 67.3 69.1 69.5 70.2 70.5 71.4 72.3 73.0 74.4 77.8 78.5 82.5 82.7 84.3 85.8 87.5 95.4
Value
Depth 1
2
3
4
5
6
7
8
9
10 11
12 13 14 15 15 14 13 12 11 10
9
8
7
6
5
4
3
2
1
Depth of
letter values
1
1
Letter
Values
#
M
F
E
D
30
15.5
8
4.5
2.5
1
55.3
53.2
51.95
50.7
69.3
77.8
83.5
86.65
95.4
Mid
69.3
66.55
68.35
69.3
73.05
Spread
22.5
30.3
34.7
44.7
Note that the mid decreased and increased indicating
a bimodal graph.
Spread
F – 22.5
E – 30.3
D – 34.7
1 – 44.7
Calculating for the quotients:
data F-spread/1.349 = 16.679
data E-spread/2.301 = 13.168
data D-spread/3.068 = 11.310
data range/ 3.726 = 11.997
```