Transcript Document

Lesson 2 - 2
Organizing Quantitative Data: The
popular displays
Objectives
• Organize discrete data in tables
• Construct histograms of discrete data
• Organize continuous data in tables
• Construct histograms of continuous data
• Draw stem-and-leaf plots
• Draw dot plots
• Identify the shape of the distribution
Vocabulary
• Histogram – bar graphs of the frequency or relative frequency
of the class
• Classes – categories of data
• Lower class limit – smallest value in the class
• Upper class limit – largest value in the class
• Class width – largest value minus smallest value of the class
• Open Ended – one of the limits is missing (or infinite)
• Stem-and-Leaf Plot – numerical graph of the data organized by
place of the digits
• Split stems – divides the digit (range) in half
• Dot plots – like a histogram, but with dots representing the bars
• Data distribution – determining from the histogram the shape of
the data
Determining Classes and Widths
The number of classes k to be constructed can be
roughly approximated by
k = number of observations
To determine the width of a class use
max - min
w = ----------------k
and always round up to the same decimal units as the
original data.
Frequency Distributions
Uniform
Skewed Right (-- tail)
Normal-like (Bell-Shaped)
Skewed Left (-- tail)
Stem & Leaf Plots Review
Given the following values, draw a stem and leaf plot
20, 32, 45, 44, 26, 37, 51, 29, 34, 32, 25, 41, 56
Ages
Occurrences
-----------------------------------------------------------------2
| 0, 6, 9, 5
|
3
| 2, 3, 4, 2
|
4
| 5, 4, 1
|
5
| 1, 6
Example 1
The ages (measured by last birthday) of the employees
of Dewey, Cheatum and Howe are listed below.
22
31
21
49
26
42
42
30
28
31
39
39
20
37
32
36
35
33
45
47
49
38
28
48
a) Construct a histogram of the ages
b) Construct a stem graph of the ages
Example 1 cont
n = 24
k = √24 ≈ 4.9 so pick k = 5
K
1
2
3
4
5
range1
20 – 25
26 – 31
32 – 37
38 – 43
44 – 50
Nr
3
6
5
5
5
Numbers of Personnel
w = (49 – 20)/5
= 29/5 ≈ 5.8  6
8
6
4
2
20-25
32-37
44-50
26-31
38-43
Ages
Example 1 cont
n = 24
k = √24 ≈ 4.9 so pick k = 5
K
1
2
3
4
5
range1
20 – 25
26 – 31
32 – 37
38 – 43
44 – 50
Nr
3
6
5
5
5
Numbers of Personnel
w = (49 – 20)/5
= 29/5 ≈ 5.8  6
8
6
4
2
20
26
32
38
Ages
44
50
Example 1: Histogram
n = 24
k = √24 ≈ 4.9 so pick k = 4
K
1
2
3
4
range1
20 – 27
28 – 35
36 – 43
44 – 51
Nr
4
8
7
5
Numbers of Personnel
w = (49 – 20)/4
= 29/4 ≈ 7.3  8
8
6
4
2
20-27
36-43
27-35
44-51
Ages
Example 1: Stem and Leaf Part
22
31
21
49
26
42
42
30
28
31
39
39
20
37
32
36
35
33
45
47
49
38
28
48
Ages of Personnel
2
0, 1, 2, 6, 8, 8,
3
0, 1, 1, 2, 3, 5, 6, 7, 8, 9, 9,
4
2, 2, 5, 7, 8, 9, 9,
Example 2
Below are times obtained from a mail-order company's
shipping records concerning time from receipt of
order to delivery (in days) for items from their
catalogue?
3
7
10
5
14
12
6
2
9
22
25
11
5
7
12
10
22
23
14
8
5
4
7
13
27
31
13
21
6
8
3
10
19
12
11
8
a) Construct a histogram of the delivery times
b) Construct a stem graph of the delivery times
Example 2: Histogram
n = 36
k = √36 = 6
12
10
w = (31 – 2)/6
= 29/6 ≈ 4.8  5
1
2
3
4
5
6
range1
2–6
7 – 11
12 – 16
17 – 21
22 – 26
27 – 31
Nr
9
12
7
2
4
2
Frequency
K
8
6
4
2
2
7
12
17
22
Days to Delivery
27
32
Example 2: Stem and Leaf Part
3
7
10
5
14
12
6
2
9
22
25
11
5
7
12
10
22
23
14
8
5
4
7
13
27
31
13
21
6
8
3
10
19
12
11
8
Days to Deliver
0
2, 3, 3, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9
1
0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 9,
2
1, 2, 2, 3, 5, 7,
3
1,
Example 2: Split Stem and Leaf Part
3
7
10
5
14
12
6
2
9
22
25
11
5
7
12
10
22
23
14
8
5
4
7
13
27
31
13
21
6
8
3
10
19
12
11
8
Days to Deliver
0
0
1
1
2
2
3
2, 3, 3, 4,
5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9,
0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4,
9,
1, 2, 2, 3,
5, 7,
1,
Time Series Plot
• Time on the x-axis
• Interested values on the y-axis
Cautions
• Label all axeses and title all graphs
• Histogram rectangles touch each other; rectangles
in bar graphs do not touch.
• Can’t have class widths that overlap
• Raw data can be retrieved from the stem-and-leaf
plot; but a frequency distribution of histogram of
continuous data summarizes the raw data
• Only quantitative data can be described as skewed
left, skewed right or symmetric (uniform or bellshaped)
Summary and Homework
• Summary
– Stem & Leaf plots maintain the raw data,
while histograms do not maintain the raw
data
– Best used when the data sets are small
• Homework:
– pg 87 - 96: 3, 6, 8, 9, 12, 14, 19, 28, 43