Summaries
7th October 2009
Session 2.3
TI-83 Notes
Making
Friends with Your Calculator
http://www.geocities.com/calculatorhelp/ti83
http://www.lrc.edu/mat/ti83_statistics.htm
http://www.math.tamu.edu/~khalman/calculator.htm
http://east.chclc.org/russo/ti3801.htm
http://www.willamette.edu/~mjaneba/help/TI-82-stats.htm
http://faculty.purduenc.edu/jkuhn/courses/previous/workbooks/301/lab1.pdf
http://instruct1.cit.cornell.edu/courses/arme210/TI83.pdf
http://www.math.oregonstate.edu/home/programs/undergrad/TI_Manuals/ti83Guidebook.pdf
http://education.ti.com/us/product/tech/83p/guide/83pguideus.html
http://education.ti.com/guidebooks/graphing/84p/TI84PlusGuidebook_Part2_EN.pdf
Key Strokes for TI83, TI84
Key List
Power/ON: Last Key on Left, Bottom Row
STAT: Center Key, 3rd Row
▲►▼◄: Toggle Keys, 2nd and 3rd Rows
ENTER: Enter/Return Key, Last Key on Right, Bottom Row
CLEAR: Clear Key, Last Key on Right, 4th Row
DEL: Delete Key, Center Key, 2nd Row
Stroke Lists for Tasks
Set Up Data
Lists: STAT, ▼▼▼▼, ENTER, ENTER
Clear Primary List L1: STAT,
ENTER, ▲, CLEAR, ▼
Edit Primary List L1: STAT,
ENTER, Enter Number, then ▼ or ENTER
Calculate Statistics for Primary
List L1: STAT, ►, ENTER, ENTER
Use Toggle Keys ▲▼to
Navigate the Statistics Screens
Descriptive Statistics Symbols
n sample
size, number of data points in the sample
mean(m,m) sample mean, sum of the data points
divided by sample size
px xth percentile,
approximately x% of the sample points are at or below px;
approximately (100-x)% of the sample points are at or above px.
p0 minimum,
0th percentile, q0 smallest value for any data point in
the sample
p25 25th percentile, q1
lower quartile, approximately 25% of the sample points are at or below p25
p50 median,
50th percentile q2 middle quartile,
approximately 50% of the sample points are at or below p50
p75 75th percentile, q3
upper quartile, approximately 75% of the sample points are at or below p75
p100
maximum, 100th percentile, q4 largest value for any
data point in the sample
Ranges and Samples
Total Sample, Total
Range: range = max min = q4 q0 = p100 p0
Upper Three-quarter
Sample, Upper Three-quarter Range = q4 q1 = p100
p25
Lower Three-quarter
Sample, Lower Three-quarter Range = q3 q0 = p75
p0
Upper Half Sample, Upper
Half Range = q4 q2 = p100 p50
(IQR)Middle Half Sample,
Middle Half Range = q3 q1 = p75 p25
Lower Half Sample, Lower
Half Range = q2 q0 = p50 p0
Upper Quarter Sample,
Upper Quarter Range = q4 q3 = p100 p75
Upper Middle Quarter
Sample, Upper Middle Quarter Range = q3 q2 = p75
p50
Lower Middle Quarter
Sample, Lower Middle Quarter Range = q2 q1 = p50
p25
Lower Quarter Sample,
Lower Quarter Range = q1 q0 = p25 p0
Example from http://www.mindspring.com/~cjalverson/_2ndhourlyfall2006versionA_key.htm
Case One
Descriptive Statistics
Serum
Creatinine and Kidney (Renal) Function
Healthy kidneys remove wastes and
excess fluid from the blood. Blood tests show whether the kidneys are failing
to remove wastes. Urine tests can show how quickly bdy
wastes are being removed and whether the kidneys are also leaking abnormal
amounts of protein. The nephron is the basic
structure in the kidney that produces urine. In a healthy kidney there may be
as many as 1,000,000 nephrons. Loss of nephrons reduces the ability of the kidney to function by
reducing the kidneys ability to produce urine. Progressive loss of nephrons leads to kidney failure. Serum
creatinine. Creatinine
is a waste product that comes from meat protein in the diet and also comes from
the normal wear and tear on muscles of the body. Creatinine
is produced at a continuous rate and is excreted only through the kidneys. When
renal dysfunction occurs, the kidneys are impaired in their ability to excrete creatinine and the serum creatinine
rises. As kidney disease progresses, the level of creatinine in the blood increases.
Suppose that we sample serum creatinine levels in a random sample of adults. Serum creatinine (as mg/dL) for each
sampled subject follows:
15.0, 14.5, 14.2, 13.8, 13.5, 13.1, 12.2, 11.1, 10.1, 9.8, 8.1,
7.3, 5.1, 5.0, 4.9, 4.8, 4.0, 3.5, 3.3, 3.2, 3.2, 2.9, 2.5, 2.3, 2.1, 2.0, 1.9,
1.9, 1.8, 1.6, 1.5, 1.5, 1.4, 1.4, 1.3, 1.3, 1.3, 1.2, 1.2, 1.1, 1.12, 1.09,
1.05, 0.95, 0.92, 0.9, 0.9, 0.9, 0.9, 0.8, 0.8, 0.8, 0.8, 0.8, 0.7, 0.7, 0.7, 0.7,
0.7, 0.7, 0.7, 0.7, 0.7, 0.6, 0.6, 0.6, 0.6, 0.6, 0.6
Compute and interpret
the following statistics: sample size (n), p00, p25, p50,
p75, p100, (p75-p00), (p100-p25),
(p75-p50), (p50-p25). Be specific and complete. Show your work, and discuss
completely for full credit.
Numbers
n=69
p0 = 0.6
p25 = 0.8
p50 = 1.3
p75 = 3.5
p100 = 15.0
p75-p0 = 3.5 0.6 = 2.9
p100-p25 = 15.0 0.8 = 14.2
p75-p50 = 3.5 1.3 = 2.2
p50-p25 = 1.3 0.8 = 0.5
Note: Another acceptable
estimate for P75 is 3.75.
n=69
p0 = 0.6
p25 = 0.8
p50 = 1.3
p75 = 3.75
p100 = 15.0
p75-p0 = 3.75 0.6 = 3.15
p100-p25 = 15.0 0.8 = 14.2
p75-p50 = 3.75 1.3 = 2.45
p50-p25 = 1.3 0.8 = 0.5
Interpretation
There are 69 subjects in
the sample. Each subject yields a serum creatinine
level.
The subject in the sample
with the lowest level of serum creatinine has .6 mg creatinine per deciliter serum.
Approximately 25% of the
subjects in the sample have .8 or less mg creatinine
per deciliter serum.
Approximately 50% of the
subjects in the sample have 1.3 or less mg creatinine
per deciliter serum.
Approximately 75% of the
subjects in the sample have 3.5 or less mg creatinine
per deciliter serum.
The subject in the sample
with the highest level of serum creatinine has 15.0
mg creatinine per deciliter serum.
Approximately 75% of the subjects in the sample have between 0.6
and 3.5 mg creatinine per deciliter serum. The
largest difference in serum creatinine between any
two subjects in this lower three-quarter-sample is 2.9 mg creatinine
per deciliter serum.
Approximately 75% of the subjects in the sample have between 0.8
and 15.0 mg creatinine per deciliter serum. The
largest difference in serum creatinine between any
two subjects in this upper three-quarter-sample is 14.2 mg creatinine
per deciliter serum.
Approximately 25% of the subjects in the sample have between 1.3
and 3.5 mg creatinine per deciliter serum. The
largest difference in serum creatinine between any
two subjects in this upper-middle-quarter-sample is 2.2 mg creatinine
per deciliter serum.
Approximately 25% of the subjects in the sample have between 0.8
and 1.3 mg creatinine per deciliter serum. The
largest difference in serum creatinine between any
two subjects in this lower-middle-quarter-sample is 0.5 mg creatinine
per deciliter serum.
The Other Ranges
p100-p0 = 15.0 0.6 = 14.4
100% of the subjects in
the sample have between 0.6 and 15.0 mg creatinine
per deciliter serum. The largest difference in serum creatinine
between any two subjects in the total sample is 14.4 mg creatinine
per deciliter serum.
p100-p50 = 15.0 1.3 = 13.7
Approximately 50% of the
subjects in the sample have between 1.3 and 15.0 mg creatinine
per deciliter serum. The largest difference in serum creatinine
between any two subjects in this upper-half sample is 13.7 mg creatinine per deciliter serum.
p75-p25 = 3.50 0.8 = 2.70
Approximately 50% of the
subjects in the sample have between 0.8 and 3.5 mg creatinine
per deciliter serum. The largest difference in serum creatinine
between any two subjects in this middle-half sample is 2.7 mg creatinine per deciliter serum.
p50-p0 = 1.3 0.6 = 0.70
Approximately 50% of the
subjects in the sample have between 0.6 and 1.3 mg creatinine
per deciliter serum. The largest difference in serum creatinine
between any two subjects in this lower-half sample is 0.7 mg creatinine per deciliter serum.
p100-p75 = 15.0 3.5 = 11.5
Approximately 25% of the
subjects in the sample have between 3.5 and 15.0 mg creatinine
per deciliter serum. The largest difference in serum creatinine
between any two subjects in this upper-quarter sample is 11.5 mg creatinine per deciliter serum.
p25-p0 = 0.8 0.6 = 0.2
Approximately 25% of the
subjects in the sample have between 0.6 and 0.8 mg creatinine
per deciliter serum. The largest difference in serum creatinine
between any two subjects in this lower-quarter sample is 0.2 mg creatinine per deciliter serum.
Example from here: http://www.mindspring.com/~cjalverson/_2nd_Hourly_Spring_2006_Key.htm
Case One
Descriptive Statistics
Maternal Body Mass Index
(BMI)
BMI is defined as the
ratio Weight/(Height2), and is one of
several measures of body size used in medicine and in public health. Consider a
random sample of mothers, US residents, all aged 35 years or older at the time
of the pregnancy, whose BMI, measured as kilograms per
meter squared (kg/m2) is measured at the beginning of the pregnancy:
19.6
25.7 19.8 20.4 22.9 26.6 19.0 30.2 20.7 21.6 21.1 27.5 19.8 23.1 23.2 20.7 23.6
24.2 26.3 42.6 23.9 17.4 20.5 20.8 19.5 21.8 27.4 21.5 17.2 27.5 22.5 19.6 20.5
24.3 24.8 26.6 20.8 24.2 22.5 31.3 22.3 25.1 23.2 20.5 22.7 25.0 23.4 19.5 20.0
20.5
Compute and interpret
the following statistics: sample size, p00, p25, p50,
p75, p100, (p75-p00), (p75-p25),
(p100-p50), (p100-p75).
Numbers
n=50; p0=17.2;
p25=20.5; p50=22.5; p75=24.8; p100=42.6;
p75 - p0=7.6; p75
- p25=4.3; p100 - p50=20.1;
p100 - p75 = 42.6 - 24.8 = 17.8
Discussion
n=50: There are 50
mothers in the sample, US residents, all aged 35 years or older at the time of
the pregnancy, whose BMI, measured as kilograms per meter squared (kg/m2)
is measured at the beginning of the pregnancy.
p0=17.2: The
mother in the sample with the lowest BMI had an initial BMI of 17.2 kg/m2.
p25=20.5:
Approximately 25% of the mothers in the sample have initial BMIs of 20.5 kg/m2
or lower.
p50=22.5:
Approximately 50% of the mothers in the sample have initial BMIs of 22.5 kg/m2
or lower.
p75=24.8: : Approximately 75% of the mothers in the sample have
initial BMIs of 24.8 kg/m2 or lower.
p100=42.6: The
mother in the sample with the highest BMI had an initial BMI of 42.6 kg/m2.
p75 - p0=7.6: Approximately 75% of the
mothers in the sample had initial BMIs between 17.2 and 24.8 kg/m2.
The largest possible difference in initial BMI between any two mothers in this
lower three-quarter sample is 7.6.
p75 - p25=4.3: Approximately 50% of the
mothers in the sample had initial BMIs between 20.5 and 24.8 kg/m2.
The largest possible difference in initial BMI between any two mothers in this
middle half sample is 4.3.
p100 - p50=20.1: Approximately 50% of the
mothers in the sample had initial BMIs between 22.5 and 42.6 kg/m2.
The largest possible difference in initial BMI between any two mothers in this
upper half sample is 20.1.
p100 - p75 = 42.6 - 24.8 = 17.8: Approximately 25% of the mothers in
the sample had initial BMIs between 24.8 and 42.6 kg/m2. The largest
possible difference in initial BMI between any two mothers in this upper
quarter sample is 17.8 .
The Other Ranges
p100 - p0 = 42.6 - 17.2 = 25.4: 100% of the mothers in the sample
had initial BMIs between 17.2 and 42.6 kg/m2. The largest possible
difference in initial BMI between any two mothers in the total sample is 17.8
p100 - p25 = 42.6 - 20.5 = 22.1: Approximately 75% of the mothers in
the sample had initial BMIs between 20.5 and 42.6 kg/m2. The largest
possible difference in initial BMI between any two mothers in this
upper-three-quarter sample is 22.1
p50 - p0 = 22.5 - 17.2 = 5.3: Approximately 50% of the mothers in
the sample had initial BMIs between 17.2 and 20.5 kg/m2. The largest
possible difference in initial BMI between any two mothers in this lower half
sample is 5.3.
p100 - p50=20.1: Approximately 50% of the
mothers in the sample had initial BMIs between 22.5 and 42.6 kg/m2.
The largest possible difference in initial BMI between any two mothers in this
upper half sample is 20.1.
p75 - p50 = 24.8 - 22.5 = 2.3: Approximately 25% of the mothers in
the sample had initial BMIs between 22.5 and 24.8 kg/m2. The largest
possible difference in initial BMI between any two mothers in this
upper-middle-quarter sample is 2.3.
p50 - p25 = 22.5 - 20.5 = 2.0: Approximately 25% of the mothers in
the sample had initial BMIs between 20.5 and 22.5 kg/m2. The largest
possible difference in initial BMI between any two mothers in this
lower-middle-quarter sample is 2.0 .
p25 - p0 = 20.5 - 17.2 = 3.3: Approximately 25% of the mothers in
the sample had initial BMIs between 17.2 and 20.5 kg/m2. The largest
possible difference in initial BMI between any two mothers in this
lower-quarter sample is 3.3 .
Case 3.1
Descriptive Statistics
Serum Creatinine
and Kidney (Renal) Function
Healthy kidneys remove wastes and
excess fluid from the blood. Blood tests show whether the kidneys are failing
to remove wastes. Urine tests can show how quickly bdy
wastes are being removed and whether the kidneys are also leaking abnormal
amounts of protein. The nephron is the basic
structure in the kidney that produces urine. In a healthy kidney there may be
as many as 1,000,000 nephrons. Loss of nephrons reduces the ability of the kidney to function by
reducing the kidneys ability to produce urine. Progressive loss of nephrons leads to kidney failure. Serum
creatinine. Creatinine
is a waste product that comes from meat protein in the diet and also comes from
the normal wear and tear on muscles of the body. Creatinine
is produced at a continuous rate and is excreted only through the kidneys. When
renal dysfunction occurs, the kidneys are impaired in their ability to excrete creatinine and the serum creatinine
rises. As kidney disease progresses, the level of creatinine in the blood increases.
Suppose that we sample serum creatinine levels in a random sample of adults. Serum creatinine (as mg/dL) for each
sampled subject follows:
35.0, 14.5, 14.2, 13.8, 13.5, 13.1, 12.2, 11.1, 10.1, 9.8, 8.1,
7.3, 5.1, 5.0, 4.9, 4.8, 4.0, 3.5, 3.3, 3.2, 3.2, 2.9, 2.5, 2.3, 2.1, 2.0, 1.9,
1.9, 1.8, 1.6, 1.5, 1.5, 1.4, 1.4, 1.3, 1.3, 1.3, 1.2, 1.2, 1.1, 1.12, 1.09,
1.05, 0.95, 0.92, 0.9, 0.9, 0.9, 0.9, 0.8, 0.8, 0.8, 0.8, 0.8, 0.7, 0.7, 0.7,
0.7, 0.7, 0.7, 0.7, 0.7, 0.7, 0.6, 0.6, 0.6, 0.6, 0.3, 0.2
Compute and interpret
the following statistics: sample size (n), p00, p25, p50,
p75, p100, (p75-p00), (p100-p50),
(p75-p25), (p50-p00).
Numbers
N
Q0
Q1
Q2
Q3 Q4
69
0.2 0.8
1.3
3.5 35
p75 p00 = 3.5 .2 =
3.3
p100 p50 = 35 1.3 =
33.7
p75 p25 = 3.5 .8 =
2.7
p50 p00 = 1.3 .2 =
1.1
Discussion
There are 69 subjects in
the sample.
The subject in the sample
with the lowest serum creatinine level has .2 mg creatinine per dL serum.
Approximately 25% of the
subjects in the sample have serum creatinine levels
of .8 mg creatine per dL
serum or less.
Approximately 50% of the
subjects in the sample have serum creatinine levels
of 1.3 mg creatine per dL
serum or less.
Approximately 75% of the
subjects in the sample have serum creatinine levels
of 3.5 mg creatine per dL
serum or less.
The subject in the sample
with the highest serum creatinine level has 35 mg creatinine per dL serum.
Approximately 75% of the
subjects in the sample have serum creatine levels
between .2 and 3.5 mg creatinine per dL serum, and the largest possible difference in serum creatinine level between any pair of subjects in this lower
three-quarter-sample is 3.3 mg creatinine per dL serum.
Approximately 50% of the
subjects in the sample have serum creatine levels
between .8 and 3.5 mg creatinine per dL serum, and the largest possible difference in serum creatinine level between any pair of subjects in this
middle-half-sample is 2.7 mg creatinine per dL serum.
Approximately 50% of the
subjects in the sample have serum creatine levels
between 1.3 and 35 mg creatinine per dL serum, and the largest possible difference in serum creatinine level between any pair of subjects in this upper-half-sample
is 33.7 mg creatinine per dL
serum.
Approximately 50% of the
subjects in the sample have serum creatine levels
between .3 and 1.3 mg creatinine per dL serum, and the largest possible difference in serum creatinine level between any pair of subjects in this
lower-half-sample is 1.1 mg creatinine per dL serum.
Part Three
Case 3.2
Descriptive
Statistics
Angry Barrels of Monkeys
A company, BarrelCorpΤ
manufactures barrels and wishes to ensure the strength and quality of its
barrels. Chimpanzees traumatized the company owner as a youth; so the company
uses the following test (Angry_Barrel_of_Monkeys_Test)
of its barrels:
Ten
(10) chimpanzees are loaded into the barrel.
The
chimpanzees are exposed to Angry!Monkey!Gas!δ,
an agent guaranteed to drive the chimpanzees to a psychotic rage.
The angry,
raging, psychotic chimpanzees then destroy the barrel from the inside in an
angry, raging, psychotic fashion.
The
survival time, in minutes, of the barrel is noted.
A random sample of 50 BarrelCorpΤ barrels is evaluated using the Angry_Barrel_of_Monkeys_Test, and the survival time
(in ***MINUTES***) of each barrel is noted. The survival time of each
barrel is listed below:
03, 05, 07, 12, 12, 14, 17, 19, 22, 23, 25, 25, 26, 26, 26,
27, 27,
28, 28, 29, 29, 30, 30, 30, 30, 30, 30, 31, 31, 32, 32, 34,
34, 35,
36, 37, 38, 38, 40, 43, 48, 51, 53, 54, 56, 57, 58, 58, 60,
62
Compute and interpret the following measures of location or dispersion: sample
size; mean, median; percentiles: 0th , 25th , 50th
, 75th , 100th ; ( P100 - P75 ) ; iqr, range
Numbers
n
Q0
Q1
Q2
Q3 Q4
50
3
26
30
38 62
p100 p75 = 62 38 = 24
p75 p25 = 38 26 = 12
p100 p00 = 62 3 = 59
Discussion
There are 50 barrels in
the sample.
The barrel in the sample
with the briefest survival survived 3 minutes of aggravated monkey damage.
Approximately 25% of the
barrels in the sample survived 26 minutes of aggravated monkey damage or less.
Approximately 50% of the
barrels in the sample survived 30 minutes of aggravated monkey damage or less.
Approximately 75% of the
barrels in the sample survived 38 minutes of aggravated monkey damage or less.
The barrel in the sample
with the longest survival survived 62 minutes of aggravated monkey damage.
Approximately 25% of the
barrels in the sample survived between 38 and 62 minutes of aggravated monkey
damage, and the largest possible difference in survival time between any pair
of barrels in this upper-quarter-sample is 24 minutes.
Approximately 50% of the
barrels in the sample survived between 26 and 38 minutes of aggravated monkey
damage, and the largest possible difference in survival time between any pair
of barrels in this middle-half-sample is 12 minutes.
100% of the barrels in
the sample survived between 3 and 62 minutes of aggravated monkey damage, and
the largest possible difference in survival time between any pair of barrels in
the sample is 59 minutes.