### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Stat Meth Res I STA 6166

FIU

GPA 3.97

### View Full Document

## 24

## 0

## Popular in Course

## 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.

## Popular in Statistics

## Reviews for Stat Meth Res I

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

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

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.