Post on 02-Jun-2018
8/10/2019 The Treatment of Children With Conduct Disorder Can Be Complex
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Probability & Statistics
Departament of Mathematics.
Descriptive Statistics
1. The treatment of children with conduct disorder can be complex. The treatment can be provided in a variety
scenarios depending upon the severity of the behavior. As well as the challenge offered by the treatment are lack o
cooperation from the boy / girl and fear and distrust of adults. In order to design a comprehensive treatment plan,
the child and adolescent psychiatrist may use information from the child, family, teachers and other medica
specialists to understand the causes of disorder. To do this, a local psychiatrist considered a random sample of 20
children, noting the time required for each child to achieve a comprehensive plan of treatment revealed th
following (in hours):
6 7 7 8 8 8 8 9 9 9
9 9 9 9 10 10 10 10 10 11
a.
With non-grouped data, find the mode, the median, re quaritles 1 and 3 and the interquartilic range
b.
Assume that each integer value represents a class. Generate frequency distribution, histogram, frequency
polygon, ogive, Pareto diagram and box plot.
2. The following data represents a population
a.
What can you say about the population?
b.
Make a sketch of the frequency distribution and the ogive
Mean 210.7954545
Typical error 17.28767416
Median 168
Mode 72
Standard Deviation 162.1727587
Variance 26300.00366
Kurtosis 0.710227939
Skewness 1.071147933
Range 708
Minimum 8
Maximum 716
Sum 18550
Count 88
8/10/2019 The Treatment of Children With Conduct Disorder Can Be Complex
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Probability & Statistics
Departament of Mathematics.
Descriptive Statistics
3. When collected the weights of 40 students of a university got the following information (for simplicity values were
rounded to the nearest pound).
Weight Count
118126 ///
127135 /////
136144 ///// ////
145153 ///// ///// //
154162 /////
163171 ////
172180 //
Para tu reporte crees pertinente que debe incluir
A histogram, an ogive and a boxplot
The mean, the mode, the median and the standard deviation. Also an estimation for the skewness and the curtosis
Summary of the information.
4. You interviewed 25 workers who lost their jobs in staff reduction of their companies, to determine the time it took
to get a job. These data you gave them to a friend and when he returned it back he gave you just this.
25
20
15
10
5
Semanas
Grfica de caja de Semanas
252015105
5
4
3
2
1
0
Semanas
Frecuencia
M ed ia 1 4. 64
Desv.Est. 5.219
N 25
Histograma (con curva normal) de Semanas
What can you interpret from this data?
8/10/2019 The Treatment of Children With Conduct Disorder Can Be Complex
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Probability & Statistics
Departament of Mathematics.
Descriptive Statistics
5. A survey was conducted to 348 undergraduate students about how much time they spend going to school. With this
data
a.
Generate the frequency distribution table
b.
Graph the histogram, frequency polygon and ogive
c.
Calculate all statistical measures with nongrouped data.
6. A study was conducted to determine the number of acceptable parts per worker in a process. With this data you
must do a boxplot.
For the boxplot you will need the five-number summary: Minimum, lower quartile, median, upper quartile
maximum.
Next locate in a line the minimum, the lower quartile, the median, the upper quartile and the maximum
The bottom and top of the box are always the first and third quartiles, and the band inside the box is always
the median.
Calculate the interquartilic range , and lower and upper limits for the whiskers
The whispers ends will be drawn according to the following rules.
If the minimum or maximum values are between [ ], the whispers will be shortened to the mnimum
and maximum.
If the minimum and maximum values are out [ ], the whispers will extend to and .
Any data not included between the whiskers should be plotted as an outlier with a dot, small circle, or star.
Example of a boxplot
7. The following data represent the tons of corn produced by fields with an experimental fertilizer.
d.
Generate the frequency distribution table
e.
Graph the histogram, frequency polygon and ogive
f.
Calculate statistical measures with grouped data (mean, variance, standard deviation, skewness and
kurtosis)
8/10/2019 The Treatment of Children With Conduct Disorder Can Be Complex
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Probability & Statistics
Departament of Mathematics.
Descriptive Statistics
8.
The normal distribution curve is very applied in different areas of statistics, so confirm whether a set of data has an
approximately normal distribution is vitally important. Many relatively complex mathematical procedures perform
this test. However there are less rigorous procedures based on descriptive statistics.
a) Histogram
This graph should have an approximate form to that of a normal distribution form. Also, the histogram must
show a bell-shaped behavior. This will show the feasibility that data behave as a normal distribution.
b) Empirical rule
States that nearly all values lie within three standard deviations of the mean in a normal distribution. About
68.27% of the values lie within one standard deviation of the mean. Similarly, about 95.45% of the values lie
within two standard deviations of the mean. Nearly all (99.73%) of the values lie within three standard
deviations of the mean.
c) Interquartile Range and standard deviation
It turns out that the interquartile range of a normal random variable is 1.34898 times its standard deviationThat is
The following data presents measurements related to the weight (in grams) of various types of motorcycle batteries. The
data show that there are manufacturers that offer lithium batteries manufactured with weight from 173 grams for 600c
bikes and weighing up to 2302 grams for larger displacement engines. Do the data approximates to a norma
distribution?
Weight
Mean 1049.9375
Median 1000
Mode 886
Standard deviation 376.4523
Variance for sample 141716.34
Kurtosis 0.370470
Skewness 0.499449
Range 2129
Minimum 173
Maximum 2302
Sum 151191
Count 144
5 data summary
Minimum 173
Lower Quartile 805.50
Median 1000
Upper Quartile 1257.75
8/10/2019 The Treatment of Children With Conduct Disorder Can Be Complex
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Probability & Statistics
Departament of Mathematics.
Descriptive Statistics
Maximum 2302
0.000
0.010
0.020
0.030
0.040
0.050
0.060
0.070
0.0800.090
0.100
0.110
0.120
0.130
0.140
0.150
0.160
0.170
0.180
0.190
0.200
0.210
0.2200.230
261.71 439.13 616.54 793.96 971.38 1148.79 1326.21 1503.63 1681.04 1858.46 2035.88 2213.29
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
0.550
0.600
0.650
0.700
0.750
0.800
0.850
0.900
0.950
1.000
261.71 439.13 616.54 793.96 971.38 1148.79 1326.21 1503.63 1681.04 1858.46 2035.88 2213.29
8/10/2019 The Treatment of Children With Conduct Disorder Can Be Complex
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Probability & Statistics
Departament of Mathematics.
Descriptive Statistics
Teoria de Probabilidad
Probabilidad
Conjunto ! set de datos que poseen una caracteristica en comun. Denotados por letra mayusculas y subconjutnos
minisculas .
Conjunto universal !! poosee todos los elements con la caracteristica deseada denotado por S.
A es un subconuto de b si solo todos los puntos de A estan en B A C B
Conjunto Vaciono contiene elementos A=
Diagrama de Venn representacion esquematica de conjuntos y sus relaciones
A c B c S
La union de a y b es el set de todos los puntos en a o b o ambos A u B
Interseccion de a y b es el set de puntos en ambos a y b AB
Complemento !! todos los puntos q estan en universe pero no en A .. Sombreado lo de afuera o
NOTA: dos conjuntos a y b son mutuamente excluyentes o discjuntos si y solo si la interseccion entre ambos es vacia.
AB=
Mn=6 Mx=11Med=8.44 Q3=10Q1=8
RIC= 2