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Ultimate test 1 study guide Chapter 1 1.1 Def Def Descriptive stat-consists of organizing and summarizing the information collected Inferential stat- uses methods that take results obtained from a sample, extends them to the population, and measure the reliability of the result Qualitative variable- allow for classification of individuals on some attribute or characteristic Quantitative variable- provide numerical measures of individuals Discrete value- quantitative variable that has either a finite number or possible values or a countable number of possible values Continuous variable- is a quantitave variable that has an infinite number of possible values that are not countable Population-group being studied Individual- person or object in a population Sample- subset of a population 1.2 Sampling PART 1 DEF AND CONCEPTS Census- list of all individuals in a population along with certain characteristics of each individual Observational study- measures the characteristics of a population by studying individuals in a sample but does not manipulate or influence the variable Designed experiment- applies a treatment to individuals, experimental units PART 2 RANDOM SAMPLES Most basic sample survey is simple random sampling n= donates sample size of population 1.3 Sampling Methods Stratified sample-obtained by separating the population into non-overlapping groups called strata then obtaining a sample from each strata Systematic sample- obtained by selecting every kth individual from a population. Chapter 2 Descriptive Stat 2.1 Organizing data Relative frequency- the proportion (or percent) of observations within a category Formula= relative frequency= frequency/ sum of all frequencies Ex. Find the relative frequency of the always category Response Frequency Never 25 Always 98 sometimes 12 Step 1: get total of frequency= 25+98+12=135 Step 2:plug in and solve= 98/135=.7259 Types of charts Bar graph- graph with bars, category on horizontal axis and frequency on vertical axis Pareto- bar graph with values from highest to lowest Pie chart- obvious 2.2 organizing data Histogram- constructed by drawing rectangles for each class of data, height of each rectangle is the frequency or relative frequency of the class. Width of each rectangle is the same and the rectangles touch each other Shapes of histograms symmetrical- even on both sides skewed left- shifts toward right (mean<median) skewed right-shifts toward left( mean> median) Stem and leaf plot-another way to represent quantitative data, made from a stem part and a leaf part Terms to remember: Size=number of observations Location=mean, median, mode Spread- range, variance, standard deviation Parameter- a summary number for a population a constant Statistic- summary for a sample variable Mean Median Mode Mean= average: formula Median- middle Mode- most frequent If I say “median” you say “index position value” Range= max- min Sum of squares: table to define variance Finding variance and standard deviation. Variance-average of squared deviations of the data points from their mean. Formula: X= data M= average n-1= degrees of freedom. How many categories you have – 1. Ex. What is the sum of squares of the data 22,23,19,28 M=mean=92/4 i x 1 22 2 23 3 19 4 28 x-M 22-23=-1 23-23=0 19-23=-4 28-23=5 (x-M)^2 1 0 16 25 So sum of squares = 1+0+16+25=42 Variance= sos/ degrees of freedom So 42/ n-1 or 42/ 4-1 = 42/3 = 14 Finding standard deviation Std= square root of variance Ex. Find standard deviation from above data set Take square root of 14= 3.74 Finding quartile ranges Median is the 50th percentile First quartile= number so that 25% is smaller and 75% are greater Third quartile= number so that 75% are smaller and 25 % greater Interquartile range= difference between 3rd and 1st quartile Q3-Q1= IQR Five Number Summaries = (min, Q1, median, Q3, max) Finding quartiles Steps for Q1= (25/100) x number of data +1 Q3=(75/100) X number of data + 1 Boxplot= a graph of the 5 number summary Shape Median Tail Symmetric Skewed right Skewed left Center of box Left of center Right of center Lower fence =Q1- 1.5(IQR) Upper fence=Q3+1.5(IQR) Chapter 3 Probability= area under curve Z scores Population z score Z= (x- population mean)/population standard deviation Sample z score Z= (x- mean)/ standard deviation Ex. Find z score Mean= 40 Population std= 11 What is the z score for 82? (82- 40)/ 11=3.818 STANDARD NORMAL CURVE Equal in length Right tail is longer Left tail is longer Finding z scores and areas Finding area to the right of a positive z score= located z score on table and use that point Ex. Find are to the right of z= +1.00 = 0.1587 Finding area to the right of a negative z score= locate z score on table then subtract point from 1 Ex. Find area to right of z=-1.25 = 1- .1056= .8944 Finding area to the left of a negative z score= locate z score on table then use point Finding area to the left of a positive z score = locate z score then 1 – point found For finding the lower and middle z scores of an area if the area is above .5 then subtract it from one. Next, take that answer and divide by 2, this gives you an upper and lower portion Now locate that half area on the chart and take the positive and negative identical z scores Finding x from z score formula Again formula: Z= (x- mean)/ standard deviation So now make it x= mean +z(standard deviation) Ex. Quiz 4 B 4B. Prob that 1Q below 110? Set up z formula Z= 110-100/ 16= .62 now find .62 z score and get the area. You will get .2676, but since you want below 110 this means the left tail This means that you are using a positive z score from the left, so subtract .2676 from 1 This gives you your answer of .7324 4A. Percent of people above 132 Use formula and set up 132-100/16= 2 Now since it is a posisitve z score from the right hence above 132 you find the area of z score 2 Now you get .0228 Now to get that to a percent multiple by 100 You get 2.28 % 4C Prob of IQ between 90 and 120 You must set up the z formula twice For 90= 90-100/ 16= -0.625, since it’s a negative z score from the left as 90 <100 (median) you just use the are found at -.625 z score, which is .2643 For 120= 120-100/16=1.25 since it’s a positive z score from the right you find the area of 1.25 z score which is .1151 Now take those add them together then subtract them from 1 4D Find IQ that separates from top 3% and bottom 97% Look at it in this fashion the top stands for right tail and bottom is left tail Since 97% would be .97 that is to large so we shall just use .03 for 3% as our area This allows you to find .0301 on the table with a z score of 1.88 Now take this 1.88 and plug in to the formula 1.88= x- 100/ 16 30.08 = x-100 130. 08 = x 130.08 rounds to 130 your answer 4E The middle 50% falls between which lower and upper IQ scores? Since the middle is 50% you need two tails so you divide by two giving you 25% This gives you .25 area, then you locate a z score for this and plug into formula You use .25 to find .67 and - .67 z scores Now set up for both, .67= x-100/16 10.72= x-100 110.72= x, 111 = x Now, -.67=x-100/16 -10.72=x-100 89.28= x and it rounds to 89 Always use percents as areas not z scores For section 3 on quiz 1B Notes if area is greater than .5 then subtract it from one and use that are