Download Review for Exam #1

Review for
Exam #1
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
1
Chapter 1
Population
the complete collection of elements
(scores, people, measurements, etc.)
to be studied
11
Sample
a subcollection of elements drawn
from a population
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
2
The Nature of Data
Definitions
Quantitative data
numbers representing counts or measurements
Qualitative (attribute ) data
nonnumeric data that can be separated into different
categories (categorical data)
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
3
Definitions
Discrete - Countable
Continuous - Measurements with no
gaps
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
4
Levels of Measurement
Nominal - names only
22
Ordinal - names with some order
Interval - differences but no ‘zero
zero’’
Ratio - differences and a ‘zero
zero’’
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
5
Critical Thinking
v Voluntary
Response Samples
v Small Samples
v Graphs
v Pictographs
v Percentages
v Loaded Questions
v Order of Questions
v Refusals
v Etc.
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
6
Methods of Sampling
Random
Systematic
Convenience
Stratified
Cluster
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
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Pearson Education, Inc.
7
Chapters 2,3
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
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33
8
Determine the Definition Values
for this Frequency Table
v Classes
Quiz
Scores
Frequency
0-4
2
5-9
5
10-14
8
15-19
11
20-24
7
v Lower Class Limits
v Upper Class Limits
v Class Boundaries
v Class Midpoints
v Class Width
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
9
Frequency Tables
Relative Freq. Table
Regular Freq. Table
Cumulative Freq. Table
Relative
Frequency
Axial
Load
Frequency
Axial Load
Axial
Load
Cumulative
Frequency
200 - 209
9
200 - 209
0.051
Less than 210
9
210 - 219
3
210 - 219
0.017
Less than 220
12
220 - 229
5
220 - 229
0.029
Less than 230
17
230 - 239
4
230 - 239
0.023
Less than 240
21
240 - 249
4
240 - 249
0.023
Less than 250
25
250 - 259
14
250 - 259
0.080
Less than 260
39
260 - 269
32
260 - 269
0.183
Less than 270
71
270 - 279
52
270 - 279
0.297
Less than 280
123
280 - 289
38
280 - 289
0.217
Less than 290
161
290 - 299
14
290 - 299
0.08-
Less than 300
175
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
10
Histogram
of Axial Load Data
60
Frequency
50
40
44
30
20
299.5
289.5
279.5
259.5
269.5
249.5
239.5
219.5
209.5
199.5
0
229.5
10
Axial Load (pounds)
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
11
Important Distributions
Normal
Uniform
Skewed Right
Skewed Left
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
12
Stem--Leaf Plots
Stem
10 11 15 23 27 28 38 38 39 39
40 41 44 45 46 46 52 57 58 65
Stem
Leaves
1
2
3
4
5
6
015
378
8899
014566
278
5
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
Mean
13
Measures of
Center
55
Median
Mode
Midrange
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
14
Calculator Basics for
Statistical Data
1. Put calculator into statistical mode
2. Clear previous data
3. Enter data (and frequency)
4. Select key(s) that calculate
x
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
15
Mean for a Frequency Table
x = 14.4
( rounded to one more
decimal place
than data )
Quiz
Scores
Midpoints
0-4
2
2
5
Frequency
5-9
7
10-14
12
8
15-19
17
11
20-24
22
7
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
16
Measure of Variation
Range
highest
score
66
lowest
score
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
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17
Measure of Variation
Standard Deviation
a measure of variation of the scores
about the mean
(average deviation from the mean)
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
18
Measure of Variation
Variance
standard deviation squared
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
19
Same Means (x = 4)
4)
Different Standard Deviations
Frequency
s= 0
7
6
5
4
3
2
1
s = 0.8
1 2 3 4 5 6 7
1 2 3 4 5 6 7
77
s = 3.0
s = 1.0
1 2 3 4 5 6 7
1 2 3 4 5 6
7
Standard Deviation
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
20
Estimation of Standard Deviation
Range Rule of Thumb
x - 2s
x
(minimum
usual value)
s≈
x + 2s
Range ≈ 4s
Range
4
=
(maximum
usual value)
highest value - lowest value
4
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
21
The Empirical Rule
FIGURE 22- 13
(applies to bellbell- shaped distributions)
99.7% of data are within 3 standard deviations of the mean
95% within
2 standard deviations
68% within
1 standard deviation
34%
34%
2.4%
2.4%
0.1%
0.1%
13.5%
x
-
3s
x
-
13.5%
x
2s
-
x
1s
x + 1s
x + 2s
x + 3s
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
22
Measures of Position
z score
Sample
Population
88
z = x -µ
σ
z = xs- x
Round to 2 decimal places
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
23
FIGURE 2 -14
Interpreting Z Scores
Unusual
Values
-3
Ordinary
Values
-2
-1
0
Unusual
Values
1
2
3
Z
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
24
Other Measures of Position
Quartiles and Percentiles
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
25
Finding the Percentile of a
Given Score
Percentile of score x =
number of scores less than x
99
• 100
total number of scores
200 201 204 206 206 208 208 209 215 217 218
percentile of 204 = 2 • 100 = 18
11
204 is the 18th percentile
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
Start
26
Finding the Value
of the
k th Percentile
Sort the data.
(Arrange the data in
order of lowest to
highest.)
Compute
k
L=
n
100
(
)
200 201 204 206 206 208 208 209 215 217 218
Find the 75th percentile.
where
(75 ) 11 = 8.75 = L
n = number of values
100
k = percentile in question
The value of thekth percentile
is midway between the Lth value
Is
L a whole
number
?
and the next value in the
Yes
sorted set of data. Find Pk by
adding the L th value and the
next value and dividing the
No
total by 2.
Change L by rounding
it up to the next
larger whole number.
The value of Pk is the
L=9
Figure 3 -6
The 75th percentile is the 9th score, or 215.
Lth value, counting
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
from the lowest
27
Quartiles
Q1 = P 25
Q2 = P 50
Q3 = P 75
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
28
Boxplot
pulse rates (beats per minute) of smokers
52
69
52
71
60
72
60
73
60
75
60
78
63
80
63
82
66
83
67
88
68
90
5 - number summary
v Minimum - 52
10
10
v first quartile Q1 - 60
v Median - 68.5
v third quartile Q3 - 78
v Maximum - 90
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
29
Boxplot
Box--and
Box
and--Whisker Diagram
60
68.5
78
90
52
50
55
60
65
70
75
80
85
90
Boxplot of Pulse Rates (Beats per minute) of Smokers
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
30
Boxplot
Bell-Shaped
Uniform
Skewed
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
31
11
11
Triola,, Essentials of Statistics, Third Edition. Copyright 2008. Pearson
Triola
Pearson Education, Inc.
32