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# Study Guide for Exam 1 221

Clarion

GPA 3.0

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## Popular in Elementary Applied Stats

## Popular in Math

This 3 page Study Guide was uploaded by Rose Notetaker on Tuesday February 16, 2016. The Study Guide belongs to 221 at Clarion University of Pennsylvania taught by Dana Madison in Winter 2016. Since its upload, it has received 17 views. For similar materials see Elementary Applied Stats in Math at Clarion University of Pennsylvania.

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Date Created: 02/16/16

Using Basic Terminology: The Hawaii Department of Tropical Agriculture is conducting a study of ready-to-harvest pineapples in an experimental field. Pineapples are the objects (individuals). If interested in the weight of the pineapples then weights is the (variables). Weight is a (quantitative) variable because it has a numerical value. If weights of all of the ready-to-harvest pineapples in the field are included in the data then we have a (population). The average weight of all ready- to-harvest pineapples in the field is a parameter. Pineapples are categorized by how they taste “poor”, “acceptable”, and “good”. In this case the taste is the “variable”. It is also a (qualitative) or (categorical) variable. Levels of Measurement: Nominal- data that consists of names, labels, or categories. There is no implied criteria by which the data can be ordered from smallest to largest. - Names Ordinal- data that can be arranged in order. However, difference between data values either cannot be determined or are meaningless. - Class rank( the rank itself is meaningful but the numerical difference between them is meaningless) Interval- data that can be arranged in order. Difference between data values are meaningful - Temperature - Dates Ratio- data that can be arranged in order. Both difference between data values and rations of data values are meaningful. Data at the ration level have a true zero. - Length of something (Can divide 6 into 18 to determine a meaning ratio - Age - Income Use a random-number table to pick a random sample of 30 cars from a population of 500 cars. We assign each car a different number between 1 and 500. Then we use the random-number table to choose the sample. Table 1 in appendix has 50 rows and 10 blocks of 5 digits each. Systematic Sampling- it is an assumed that the elements of the population are arranged in some natural sequential order -then select a random starting point and select every kth element for our sample - Ex: people lining up to buy rock concert tickets are “in order” - This should not be used when the population is repetitive or cyclic in nature. For example, consider a fabric mill that produces dress material. Suppose the loom that produces the material makes a mistake every 17th yard, but we check only every 16th yard with an automated electronic scanner. In this case, a random starting point may or may not result in detection of fabric flaws before a large amount of fabric is produced. Cluster Sampling- method used extensively by government agencies and certain private research organizations - Begin by dividing the demographic area into sections then randomly select sections or clusters, every member of the cluster is included in the sample Frequency tables- partitions data into classes or intervals and shows how many data values are in each class. The classes or intervals are constructed so that each data value falls into exactly one class - Quantitive data - Usually broken into 5-15 classes - Find the class Width - Class Width= Largest value- smallest value/desired # of classes (always increase this answer by one) Ex: 47-1/6 = 7.7 (increase to 8) Lower Class Limit- lowest data value that can fit in a class Upper Class Limit- highest value that can fit into a class Class Width- difference between the lower class limit of one class and the lower class limit of the next class The smallest distance is 1 in this scenario so it is the lower class limit. Since the class width is 8 we add 1 to 8 so the lower class limit for the second class in 9 Tallying data- method of counting data values that fall into a particular class or category Class Frequency- number of tally marks corresponding to that class (# of tally marks) Midpoint- middle of each class, often used to representative value for the whole class Midpoint= lower class limit + upper class limit/2 Class Boundaries- space between upper limit of one class and lower limit of the next To find the Upper Class Boundaries add 0.5 unit to the upper class limits To find the Lower Class Boundaries subtract 0.5 from the lower class limits Relative Frequency- the proportion of all data values that fall into that class Relative Frequency= f/n=Class frequency/Total of all Frequencies Ex: 14/60 =.23 for the first class Histograms and Relative Frequency Histograms - Bars are used to represent each class or relative frequency 1) Make a frequency table 2) Place class boundaries on horizontal axis and frequencies or relativities on vertical axis 3) The height of the bar is the frequency the width is the boundary Distribution Shapes 1) Mound-shaped symmetrical - Both sides of the graph or about the same if folded in half (symmetrical) 2) Uniform or rectangular - Every class has an equal frequency 3) Skewed left or skewed right - When the higher frequency are one side of the graph 4) Bimodal - When two classes with the largest frequencies are separated by at least one class Mode- value that occurs the most frequently Median- central value Mean- sum of all entries/# of entries Range- difference between largest and smallest values Chebyshev’s Theorem For any set of data and for any constant k greater than 1 proportion of the data that must lie within k standard deviations on either side of the mean is at least 1- 1/k 2 Interquartile range= Q3 –Q1

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