Post on 06-Jan-2016
description
Statistic for the day:Tons of gold turned into wedding
rings each year in US: 17Source: Goldfield Mineral Services (London)
Assignment:Exercises page 123-125: 5, 6, 10, 12, 14, 15
These slides were created by Tom Hettmansperger and in some cases modified by David Hunter
Statistic for the day (the sequel):Hours prior to the start of class I’ll try to have the lecture notes
posted online: 8
Source: A voice inside my head
Turning Data into Information: The distribution of the data The shape of the distributionThe shape of the distribution
Is it skewed or is it symmetric?Is it skewed or is it symmetric? What is a typical value?What is a typical value?
Should we use the mean or the median?Should we use the mean or the median? What is the spread of the distribution?What is the spread of the distribution?
Should we use the standard deviation or the Should we use the standard deviation or the interquartile range? interquartile range?
What are the quartiles?What are the quartiles?
Age at Death of English Rulers
60, 50, 47, 53, 48, 33, 71, 43, 65, 34, 60, 50, 47, 53, 48, 33, 71, 43, 65, 34, 56, 59, 49, 81, 67, 68, 49, 16, 86, 6756, 59, 49, 81, 67, 68, 49, 16, 86, 67
Turning this data into information.
Shape: Stem and Leaf Display 1 1 6
1 2
3 3 34
8 4 37899
(4) 5 0369
8 6 05778
3 7 1
2 8 16
The Median and the Quartiles
16 33 34 43 47 * 48 49 49 50 53**56 59 60 65 67***67 68 71 81 86
Q1 M Q3
The first quartile is the number that divides the data into the firstquarter and the last three quarters.
The median divides the data into halves.
(5) (5) (5) (5)
5 Number Summary
Median M = 54.5Median M = 54.5 First Quartile Q1 = 47.5First Quartile Q1 = 47.5 Third Quartile Q3 = 67Third Quartile Q3 = 67 Lowest = 16Lowest = 16 Highest = 86Highest = 86
Graphical of 5 number summary: Boxplot
10
20
30
40
50
60
70
80
90
age
Age at death of a sample of 20rulers of England
Anatomy of a Boxplot
10
20
30
40
50
60
70
80
90
age
Age at death of a sample of 20rulers of England
IQR = Q3 - Q1
(whiskers)Reasonable range of data
Outlier
Q1
Q3
M
Interpretations:
Median is a Median is a typical valuetypical value.. Interquartile range = Q3 – Q1 and is a measure of Interquartile range = Q3 – Q1 and is a measure of
spreadspread of the data. It is the width of the middle of the data. It is the width of the middle 50% of the data.50% of the data.
Two data sets may differ in Two data sets may differ in shapesshapes, , typical typical valuesvalues (medians) or in (medians) or in spreadsspreads (IQR) or all three. (IQR) or all three.
RESEARCH QUESTIONS WHEN RESEARCH QUESTIONS WHEN TRANSLATED INTO STATISTICAL TRANSLATED INTO STATISTICAL QUESTIONS BECOME: ARE THE QUESTIONS BECOME: ARE THE DIFFERENCES SIGNIFICANT?DIFFERENCES SIGNIFICANT?
Question: Do men have larger handspans than women?
Handspan: Distance in centimeters from tip of thumb to
tip of little finger.
What sort of study?
Data
Men (n = 78) 23.5 22.5 23.5 23.0 24.5 20.5 22.0 22.0 22.5 21.5 24.5 24.5 21.0 21.0 20.5 22.0 22.0 19.0 22.0 22.0 20.0 21.0 21.5 22.5 22.5 24.5 24.0 23.5 20.0 22.5 24.0 21.0 23.0 23.0 22.5 21.5 20.5 20.5 21.5 20.5 21.0 22.5 21.0 22.0 23.0 21.0 24.0 22.0 21.0 21.0 23.0 24.0 22.0 22.5 21.5 23.5 22.0 18.0 23.5 24.0 24.5 23.0 22.5 24.5 22.0 22.0 24.5 24.0 21.5 22.0
Women (n = 89) 21.5 18.0 20.0 21.0 20.5 18.5 21.0 19.5 20.0 18.5 20.5 18.5 18.0 19.5 21.0 20.0 20.0 19.0 17.0 17.5 19.0 18.5 20.5 19.5 20.0 20.0 18.5 20.0 21.0 19.5 20.0 20.0 21.5 18.5 23.0 20.5 16.5 19.5 18.5 18.5 20.0 21.0 20.5 21.5 21.5 21.0 19.0 20.5 20.5 19.5 19.5 19.0 20.5 20.0 21.5 19.0 19.0 20.0 19.5 20.0 16.0 17.5 19.5 22.5 20.0 20.5 19.0 19.5 19.0 20.0 18.5 20.0 22.0 17.0 18.5 21.0 20.5 19.0 20.5 18.5 19.0 19.0 20.0 17.0 18.5 20.0 17.0 18.5 21.0
Female Male
15 20 25
0
10
20
HandSpan
Fre
que
ncy
Female Male
16
17
18
19
20
21
22
23
24
25
26
Sex
Ha
ndS
pan
5-number Summaries
LowLow FirstFirst
QuartileQuartile
MedianMedian ThirdThird
QuartileQuartile
HighHigh
MalesMales 1818 2121 2222 2424 2626
FemalesFemales 1616 1919 2020 2121 2323
Male IQR = 3 Female IQR = 2