The Treatment of Children With Conduct Disorder Can Be Complex

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


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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?


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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)


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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


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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


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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

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The Treatment of Children With Conduct Disorder Can Be Complex