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## Stat Meth Res I

by: Jonatan Kunde

24

0

5

# Stat Meth Res I STA 6166

Jonatan Kunde
FIU
GPA 3.97

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
5
WORDS
KARMA
25 ?

## Popular in Statistics

This 5 page Class Notes was uploaded by Jonatan Kunde on Monday October 12, 2015. The Class Notes belongs to STA 6166 at Florida International University taught by Staff in Fall. Since its upload, it has received 24 views. For similar materials see /class/221818/sta-6166-florida-international-university in Statistics at Florida International University.

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Date Created: 10/12/15
Computing Descriptive Statistics Sample 1 First Second Third Fourth Fifth Sixth List the observations in the sample 2 3 3 4 4 4 5 5 6 Beneath or next to each sample value put its rank The smallest value will have rank 1 and the largest will have rank n where n the number of observations in the sample sample 2 3 3 4 4 4 5 5 6 ranks l 3 2 4 5 6 7 8 9 Since two of the observations have the value 3 the first one is given rank 2 and the second one is given rank 3 Each value is given a unique rank Compute the sample range H L 6 4 Graphically display the data Since this is a small sample with repetitions I have used a line graph For larger data sets s stemplot should be used For really large samples let SPSS do the work for you You will still need to be able to answer the questions frequency OI NUer l 2 3 4 5 6 7 The values on the vertical axis are the frequencies and the values on the horizontal axis are the values of the observations Try to describe the shape of the distribution In this case we have a symmetric distribution with a single mode Distributions like this are often called quotmound shapedquot distributions Locate the median n1 10 ML 5 Therefore the median is the value with rank 5 In this case the value with rank 5 is 4 Hence M Seventh Note Sample 2 First Second Third Fourth Compute the mean variance and standard deviation of the sample These values are based not on the order of the observations but on the actual values of the observations We need the following information n Xx and 2x3 n9 2x36 2x2156 X The sample mean is XZ 4 11 9 We will use the computational formula rather than the definition to compute the sample variance Both your text and ActivStats give the definition and use it in the examples However they assume you will be using a software package such as SPSS to do most of your computation For testing purposes we will use the computational formula 2 X 32 n 15 n l 8 8 The standard deviation is the square root of the variance S SZ l 5 122 For a larger sample we would also give the 5 number summary and check for outliers List the observations in the sample 2 3 2 3 4 6 4 6 5 5 Beneath or next to each sample value put its rank sample 2 3 2 3 4 6 4 6 5 5 ranks l 3 2 4 5 9 6 10 7 8 Compute the sample range H L 6 4 Graphically display the data frequency 3 2 l O x l 2 3 4 5 6 7 Fifth Sixth Seventh Note Try to describe the shape of the distribution In this case we have a symmetric distribution with no mode Distributions like this are called quotuniformquot distributions Locate the median ML ITEL 5 5 Therefore the median is the average of the values with ranks 5 and 6 In this case the value with rank 5 is 4 and the value with rank 6 is also 4 Hence M 4 Compute the mean variance and standard deviation of the sample We need the following information n Xx and2x3 nlO 2x40 2x2180 X The sample mean is X2 4 0 4 n 10 We will use the computational formula rather than the definition to compute the sample variance 2 Extgzx 180 402 52 n 10 222 n l 9 9 The standard deviation is the square root of the variance SVS VZ22l49 NOTEV222l4907ll985 22214899643 These values are not the same For larger sample we would also give the 5 number a summary and check for outliers The following examples are done without commentary to show you how I expect your answers to be written Sample 3 2 3 2 4 6 5 6 rank 1 3 2 4 6 5 7 frequency 3 2 n7 2x28 2x2130 l R H L 6 2 4 O x l 2 3 4 5 6 7 MLn l 4 therefore M 4 2 2 X XE 4 n 7 2 X 2 ZXLL 13mg 18 52 n 3 n l 6 6 s s 173 This distribution is bimodal and has a quotbathtubquot shape Sample 4 4 5 4 6 8 7 8 rank 1 3 2 4 6 5 7 frequency 4 3 2 n7 42 2x2270 l R H L 8 4 4 O l 2 3 4 5 6 7 8 9 x ML n 4 therefore M 6 2 2 X XE426 n 7 X 2 ZX2E 27o 18 52 n 3 n l 6 6 s s2 173 This distribution is also bimodal and has a quotbathtubquot shape Some What What What questions to ponder do these samples have in common The range of each sample is 4 The distribution of each sample is symmetric The mean of each sample is the same as its median do samples 1 3 have in common besides the range These samples have both mean and median equal to 4 do samples 3 and 4 have in common besides the range They have the same variance and standard deviation They also have the same shape How do these samples differ Samples 1 3 have different sample sizes The variances and standard deviations of samples 1 3 are different The distributions of samples 1 3 have different shapes How do the values in sample 4 compare to tho e in sample 3 T 5 he values in sample 4 were obtained by adding 2 to each value in sample 3 that is x4 x3 2 x 6 and x 4 Hence x x 2 M4 6 and M3 4 Hence M4 M3 2 For any linear transformation of the data the measures of central tendency of the new variable are the linear transformations of the measures of central tendency of the original The 4 graphs are given below As the number of values away from the mean increases the variance increases Sample 1 Sample 2 frequency frequency 4 3 3 2 2 l l O x O l 2 3 4 5 6 7 l 2 3 4 5 6 7 52 222 52 15 Sample 3 Sample 4 frequency frequency 3 4 2 3 l 2 O x l l 2 3 4 5 6 7 O l 2 3 4 5 6 7 8 9 X

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