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| observations (such as measurements, genders, survey responses) that have been collected |
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| A collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data |
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the complete and entire collection of elements (scores, people, measurements) to be studied EX: set of all JCC students all Mexican-Americans in jefferson county, KY all DVR owners in the US |
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the collection of data from every member in a population. |
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a subcollection of elements drawn from a population. EX: 5,000 randomly selected TIVO owners a poll of 576 Mexican-American residents of Jefferson County KY |
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a numerical measurement describing some characteristic of a population population<--->parameter EX: average weekly cost of gasoline used by all JCC students in commuting to campus |
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a numerical measurement describing some characteristic of a sample sample<--->statistic EX: Average weekly cost of gasoline used by 100 randomly selected JCC students in commuting to campus |
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can be separated into different categories that are distinguished by some nonnumeric characteristic EX: political party, gender, religious affiliation, blood type, etc. |
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consists of numbers representing counts or measurement |
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A set number EX: 12 finalists on the television show "American Idol" 693,604 citizens in Metro Louisville |
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The set of natural numbers {1,2,3,4,5,6,7,8,9...} |
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numerical data results from either a finite or a countable number of possible values- countable number EX: Gold medals won by American athletes in 2008 Olympic Games Number of Vivanno smoothies sold today at Starbucks on Dixie |
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numerical data results from infinately many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps- can be measured EX: amount of gasoline in a fule tank: 12.5 gal, 3.4565 gal, 2 gal, 0.2 gal Body temperature:98.6, 100.32075 |
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| Nominal Level of Measurement |
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chracterized by data that consist of names, labels, or categories only. these categories connot be arranged in an ordering scheme (such as low to high) cannot be averaged because they have no numerical value or ordering EX: Religious affiliations, rental car companies, numbers that assign lables like zip codes social security numbers or phone numbers |
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| Ordinal Level of Measurement |
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involves data that may be arranged in some order, but differences between data values either cannot be determined or are meaningless EX: band ratings of superior, excellent, good, fair, poor; gold, silver, and bronze medals at the olympics, 1st, 2nd, and 3rd place at a pagent, basketball team rankings |
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| Interval Level of Measurement |
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like the ordinal level, with the additional property that we can draw meaningful amounts of differences between data there is NO inherent (natural) zero starting point (where none of the quantity is present) EX: Temperatures of 25 degrees and 50 degrees (difference of 25 degrees but 50 is not double 25) Years 1000, 2000, 1776, 1944. Time did not begin at zero- 2000 is not twice as much as 1000 although it is 1000 years older. |
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| Ratio Level of Measurement |
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actually the interval modified to include the inherent zero starting point (where zero indicates none of the quantity is present) For values at this level, differences and ratios are meaningful EX: Temperatures in degrees Kelvin (the Kelvin temp scale started at absolute zero) Height of a tomato plant in a garden |
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observe and measure specific characteristics, but we dont attempt to modify the subjects being studied EX: Bone density tests performed on group of elderly patients with osteopotosis a gallup poll is conducted to obtain Americans opinions on the Iraq War |
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Type of observational study data are observed, measured, and collected at one point in time |
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| Retrospective (case-control) Study |
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Typoe of ovservational study data are collected from the past by going back in time (through examination of records, intervies, and so on) |
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| Prospective (longitudinal or cohort) Study |
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Type of observational study data are collected in the future from groups (called cohorts) sharing common factors |
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apply some treatment and then proceed to observe it's effects on subjects EX:clinical trial of the sleeping pill Rozerem |
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occurs in an experiment when the experimenter is not able to distinguish between the effects of different factors EX: Taking a colesterol drug and adjusting eating and exercise habits- what attributes to the drop in cholesterol? |
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| a technique in which the subject doesn't know whether he or she is recieving a treatment or a placebo |
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| neither the subject nor the person administering the treatment/placebos know who recived the treatment and who recieved the placebo |
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use this design is conductiing and experiment od testing one or more different treatments, and there are different groups of similar subjects, but the groups are different in ways that are likely to affect the responses to treatment. 1. Form blocks or groups of subjects with similar characteristics 2. Randomly assign treatments to the subjects within each group |
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repetition of an experiment used effectively when we have enough subjects to recognize differences from different treatments |
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| members of the population are selected in such a way that each individual member has an equal chance of being selected |
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of size n subjects selected in such a way that every possible sample of size n has the same chance of being chosen |
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| involves selecting memebers from a population in such a way that each member has a known (but not necessarily equal) chance of being selected |
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| Examples of Simple Random Samples |
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Military Draft- Each birthday is placed in a bowl an has equal chance of being selected Lottery- each # in the KY lottery's pick 3 game, 000-999- equal chance of selection Taking a survey of 30 JCC college algebra students- give each student a number than use a computer to randomly select 30 numbers- surevey those students whose numbers are chosen |
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sample obtained by dividing the population into at least 2 different subgroups that share the same characteristics (such as gender or age bracket) then draw a sample from ech subgroup (stratum) EX:400 men and 400 women interviewed for their opinion for presidential candidates |
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sample obtained by selecting some starting point and then selecting every kth (such as every 50th) element EX: randomly pick a name in the phone book, then pick every 100th name thereafter quality control tech;s inspect the door molding on every 5th toyota camry that comes off the assembly line |
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sample obtained by using results that are readily available EX: teacher asks how many students in the room are left handed viewers of a show are asked to go online and vote in a poll about the show |
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sample obtained by dividing the population area into sections (clusters), randomly selection some of those clusters, and then choosing all members from those selected clusters EX: satisfaction survey of JCC students- survey forms given to all students in classes that meet at 10:35am, 12:00 pm, 5:54 pm and 7:10 pm |
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professional pollsters and gov. researchers often collect data by using some combination of the five methods. involved the selection of a sample in different stafes that might use different methods of sampling |
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the difference between the sample result and the true population result; such an error results from chance sample fluctuations |
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| occurs when the sample data are incorrectly collected, recorded, or analyzied (such as by selecting a biased sample, using a defective measurement instrument, or copying the data incorrectly) |
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| Voluntary Response Sample |
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the respondants themselves decide whether or not to be included |
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questions intentionally worded to elicit a desired response |
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| indicates that two variables are related |
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| Data Characteristics: Center |
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| A representative or average value that indicates where the middle of the data set is located |
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| Data Characteristics: Variation |
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| A measure of the amount that the data values vary among themselves |
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| Data Characteristics: Distribution |
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| The nature or shape of the distribution of the data (such as bell-shaped, uniform, or skewed) |
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| Data Characteristics: Outliers |
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| Sample values that lie very far away from the vast majority of the other sample values |
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| Data Characteristics: Time |
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| changing characteristics of the data over time |
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| Frequency Distribution(table) |
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| lists data values (either individually or by groups of intervals) along with their corresponding frequencies (or counts) |
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| for a particular class- the number of original values that fall into that class |
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| the smallest numbers that can belong to the different classes |
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| the largest numbers that can belong to the different classes |
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| the numbers used to separate classes, but without the gaps created by class limits. Center of the gap between boundaries |
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| the values in the middle of the classes. Each class mid-point can be found by adding the lower class limit to the upper class limit and dividing the sum by 2 |
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| the difference between two consecutive lower class limits or two consecutive lower class boundaries |
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| found by dividing each class frequency by the total of all frequencies |
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| Relative Frequency Distribution |
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| includes the same class limits as the frequency distribution, but relative frequencies are used instead of actual frequencies |
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| for a class- the sum of the frequencies for that class and all previous classes |
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| a bar graph in which the horizontal scale represents classes of data values and the vertical scale represents frequencies. the heights of the bars correspond to the frequency values, and the bars are drawn adjacent to each other (without gaps) |
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| Relative Frequency Histogram |
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| has the same shape and horizontal scale as a histogram, but the vertical scale is marked with relative frequencies instead of actual frequencies |
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| uses line segments connected to points located directly above class midpoint values. |
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| a line graph that depicts cumulatice frequencies |
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| consists of a graph in which each data value is plotted as a point (or dot) along a scale of values |
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| Stemplot (Stem-and-Leaf Plot) |
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| represents data by separating each value into two parts: the stem (such as the left most digit) and the leaf (such as the rightmost digit) |
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| a bar graph for qualitative data, with bars arranged in order according to frequencies. Tallest bar left, smallest to the right |
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| a graph depicting qualitative data as slices of a pie. Each slice is properly proportioned |
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| Scatterplot (Scatter Diagram) |
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| a plot of paired (x,y) data with a horizontal x-axis and vertical y-axis. The data are paired in a way that matches each value from one data set with a corresponding value from a second data set. |
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| graph of time series data, which are data that have been collected at different points in time. |
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