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STAT 200: Exam 1 Study Guide

by: Alicia Polcha

STAT 200: Exam 1 Study Guide STAT 200

Marketplace > Pennsylvania State University > Statistics > STAT 200 > STAT 200 Exam 1 Study Guide
Alicia Polcha
Penn State
GPA 4.0

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About this Document

These notes will cover the information needed for our next exam. This includes all of chapters 1.1-3.3.
Elementary Statistics
Prof. Justin Keller
Study Guide
Statistics, Math, Stats, Business Math, mean, average, standard deviation
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This 4 page Study Guide was uploaded by Alicia Polcha on Tuesday February 2, 2016. The Study Guide belongs to STAT 200 at Pennsylvania State University taught by Prof. Justin Keller in Spring 2016. Since its upload, it has received 53 views. For similar materials see Elementary Statistics in Statistics at Pennsylvania State University.


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Date Created: 02/02/16
STAT 200 Chapters 1­4: Study Guide Exam Date: February 5, 2016 1. Chapter 1.1: a. Identify the variable in the study and determine the level of measurement: b. Quantitative: Numerical value based on measurement c. Qualitative: color, gender, personality, category, labels d. Nominal: consists of names, labels, and categories; no implied data of  which it can be ordered from small to large e. Ordinal: data can be arranged in order f. Interval: data can be arranged in order and differences in data are  meaningful g. Ratio: can be arranged in order, both differences between data values and  ratio values are meaningful; the value of zero is meaningful h.   Examples i. Time of first class  interval, quantitative ii. Score on last exam out of 100  ratio, quantitative iii. Age of student  ratio, quantitative iv. Course evaluation (poor, acceptable, ect)  ordinal, qualitative v. Length of time to complete exam  ratio, quantitative vi. Length of trip  ratio, quantitative vii. Size of fish (small, medium, large)  ordinal viii. Species of fish  nominal, qualitative ix. Number of fish caught  ratio, quantitative x. Major field of study  nominal, qualitative 2. Chapter 1.2: a. Parameters vs Statistics i. Population: set of all individuals we would be interested in  collecting data from ii. Samples: only some of individuals of interest 1. The ones we can collect data from iii. Examples:  1. Average age of all trees between 500 and 700 years a. Parameter: applies to every individual in population  “ALL TREES” in population 2. Samples of 56 trees are estimated and average age was 623  years a. Sample statistic: only some trees (56) were sampled b. Sampling Techniques: i. Simple Random Sample: Completely random; all collection of n is  equally the same ii. Stratified Sampling: divide into groups called strata based on  specific characteristics 1. Can be based on age, income, profession, ect. iii. Cluster sampling: divide populations into existing segments or  clusters (geographically) iv. Systematic Sampling: number all members sequentially; choose a  random starting point; select every kth member of population to be part of the sample v. Convenience Sampling: create sample by using data form  populations members that are readily available 1. Example: putting a survey in a public place for any  individual to fill out at their convenience 3. Chapter 1.3: a. Collecting Data: i. Observational Study: a researcher measures variables of interest  without changing anything in the study… all existing conditions  remain untouched ii. Experiment: a researcher assigns a treatment to observe the  reaction or response; in other words, a variable is used and its  effectiveness is measured iii. Examples 1. Cartons of Milk are opened; the volumes of the contents are measured a. Observational Study 2. Studying how patients respond when given a placebo a. Experiment 4. Chapter 2.1: a. Review Week 2 Notes  b. Constructing a Frequency Table i. Decide on a number of classes between 5 and 15 ii. Calculate the class width 1. (Highest Value­Lowest Value) / (# of Classes) a. (# of Classes)  What was chosen in step one b. then, increase this value of class width to the next  highest whole number.  c. NOTICE: Even if it is an exact whole number, you  will still increase it to the next highest.  i. Example: 1. 6.0  7 iii. Find all lower class limits by starting with the lowest data value  and successively adding the class width iv. Find all upper class limits by stopping at the whole number just  below the lower limit of the next highest class v. EXAMPLE ( class width = 5 ) 1. Class Width Lower Limit Upper Limit a. 92 96 b. +5 97 101 c. +5 102 106 d. Continue until you reach the “Number of Classes”  you need, which was chosen in Step One. vi. To find Frequency: 1. Go row by row through the table of numbers given to find  all numbers between specific lower and upper limit. Cross  values out each time so you do not recount a number. a. Example: From example above, the first set is from  82­86. Count all numbers in the table between these two numbers (82­86), this will represent the  frequency. vii. Understand for exam: 1. Class limits 2. Class boundaries 3. Class midpoint 4. Class width 5. Frequencies 6. Relative frequencies a. (Frequency/n) i. “ % of the whole “ ii. (Class Frequency/ total of all frequencies) 7. Cumulative frequencies a. Total of all frequencies at or below this class. 8. Relative cumulative frequencies 5. Chapter 3: a. Mean: average of all data i. Add all data in the set and divide by number of data values b. Median: order numbers in set from least to greatest…middle number is the median c. Mode: most frequently existent number in the data set d. Trimmed Mean i. 1, [1, 1, 1, 2, 2, 2, 3, 3, 3, 8, 9, 25, 26, 26, 26, 30, 50,] 100 ii. n = 20 iii. mean = (Σx) / 20 = 16 iv. 5% trimmed mean: 1. 0.05 x (20) = 1 (Remove highest and lowest ONE value) v. 10% trimmed mean: 1. 0.1 x 20 = 2 (Remove highest and lowest two values) 2. (Σx) / 16 = 12.166 e. Range: largest number in data set minus the smallest number in data set 6. Chapter 4: a. The Coefficient of Variation: i. C.V. = S / x(bar) ii. X(bar)  Mean of data b. Chebyster’s Theorem: For any set of numbers with mean x(bar) and  standard deviation, S, atleast (1 – (1/ k^2) x 100%) of those numbers must  fall between [x(bar) – kS] and [x(bar) + kS] c. Five Number Summary (displayed below) Quartiles: specific values that attempt to divide quantitative data into four equal parts. 1. find median 2. take median of lower half and upper half 3. then you will find the three medians, therefore dividing the data into four  equal parts Quartiles: also known as the fifth­number summary Q0 (zeroth quartile)  lowest data value Q1, Q2, Q3  median values Q4 (fourth quartile)  highest number in the data set Finding the quartiles 1. write down the low and high values for Q0 and Q4 2. find the median of the data (Q2) 3. find the median of the lower half not counting the median itself, to obtain Q1 4. find the median of the upper half not counting the median itself to obtain Q3


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