C127 Lecture 5 Notes- Density and Data Analysis 2-11-16 ∙ Learning goals

How different do two limited sets of data need to be before we can safely say they are different?

o Learn how to design an experiment to give best possible results

o Learn how to use standard deviation to examine quality of data sets

o Learn how to use t-test in Excel to decide if 2 experiments gave same or different results ∙ Safety/Waste Disposal

o Goggles and appropriate clothing required

o All solutions can be put down sink with plenty of water

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∙ Lab Info

o 2 solutions with different amounts ��������

Systematic error always makes data?

o Measure 2 unknowns, use t-test to make hypothesis to say whether solutions are the same density o For this lab, density concept not very important; focusing on analyzing data sets

o To get accurate data we need:

▪ Accurate mass- analytical balances (with doors on sides) go to 4 decimal places- keep in mind they have  mass limit

▪ Accurate volume- choose glassware based on what is available/best-suited

∙ Beakers- mass produced; measurements very very approximate; never measure with beakers ∙ Same goes for Erlenmeyer flasks

∙ Graduated cylinder- not best overall choice (not calibrated), but good; pick one closest in size to  amount of liquid you need

What is the percent error?

∙ Volumetric pipets/flasks- best choices for accurate and reproducible volume; made to be accurate  and precise through individual calibration; known as Class A glassware If you want to learn more check out What is the process of evolution?

∙ Quality of Data

o All data has error

o Exclude data if there is some major mistake; repeat step(s) to replace bad data

o Random error- equally likely to give high result as low; cannot get rid of it

o Systematic error- always makes data high or always makes it low; cannot identify unless you know what a  value should be (ie. theoretical yield, you spilled something); can be reduced as much as possible o ALWAYS ON EXAMS- random error always present; will ask about differences between two kinds and how to  know if systematic is present

o Percent error- when true value known:

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o When true value not known, use statistics

▪ Standard deviation �� = √∑(����−��̅)2 If you want to learn more check out Which is the no 1 country in world?
If you want to learn more check out What is a ghost light in the theater?
We also discuss several other topics like What’s the most important resource?
Don't forget about the age old question of Which between a higher or lower roe is better?
If you want to learn more check out What defines a function?

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▪▪ When scale on axis based on numbers (not ��), wider curve = more random error, narrower curve = less;  always looks same based on ��

▪ Our data sets will be much smaller; not a nice curve

▪ For us, justified to throw out data beyond ±2�� due to small sample size instead of typical ±3�� o How different do two limited sets of data need to be before we can safely say they are different? (use T-test)