Report 1 Statistical Analysis of Data Phyisc 211 (2)

8/18/2019 Report 1 Statistical Analysis of Data Phyisc 211 (2)

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CALIFORNIA STATE UNIVERSITY, LOS ANGELES

Department of Phys!s an" AstronomyPhys!s#$$ % Se!ton $&' $(&)*

Statistical Analysis of Data

Prepare" +y Ro"ney P-.a"aDane/ V!tora

Performan!e Date T-es"ay,0an-ary ), #1$2S-+msson D-e T-es"ay, 0an-ary $3, #1$2

Professor Yese 04 Fe/peTh-rs"ay $&1 pm4 5 311 p4m4

0an-ary #1$2


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Experiment No 1: Statistical Analysis of Data

I. PURPOSEPerforming this laboratory successfully will allow us to learn an important of statistical techniques as mean, standard deviation, standard deviation of themean. Also, we learn to graph a histogram from our results.

II. INTRODUCTION

ean is the average of all values of X. This is the same as for small data sets. The mean may not be a fair representation of the data, because the average iseasily inuenced by outliers (very small or large values in the data set that arenot typical. Therefore, the mean shows us an appro!imate value who is in thealmost in the middle of our data. The mean is the mathematical average of all

the terms, so it provides a basis for determining an average when necessary. To"nd it, add the values of all the terms and then divide by the number of terms.

Stan!ar! !e"iation (# is a measure of how spreads out numbers are.

The standard deviation is a numerical value used to indicate how widelyindividuals in a group vary. $f individual observations vary greatly from thegroup mean, the standard deviation is big% and vice versa. $t is important todistinguish between the standard deviation of a population and the standarddeviation of a sample. They have di&erent notation, and they are computeddifferently. The standard deviation of a population is denoted by # and thestandard deviation of a sample, by s. The 'Population tandard )eviation'*

The 'ample tandard )eviation'*


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Stan!ar! !e"iation of t#e ean $S%

&isto'ram is a bar graphin which the hori+ontal scale represents classes of data values and the verticalscales represents frequencies. The heights of the bars correspond to thefrequency values, and the bars are drawn adacent to each other (withoutgaps. The histogram shows to analy+e how much data we have in one classthat we determine to see the precision of our data.


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III. DATA AND ANA()SIS Table -o * /!periment for releasing 0 marble from the curved trac1

point2

X# 3!4

!# 5

6.6 45.7 7.585 8.6 4.7 5.68

0 59 4.: 5.5:

; 59.5 4.0 .


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Table -o 5 * /!periment for releasing one marble 0 times from the curvedtrac1

point2

X# 3!4

!# 5

0.8 47.< :7.7<5 :.< 4:.8 0;.6

0 :.7 4:.6 00.


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,.1. -rom Tale No 0 : Experiment for releasin' one marle ,1times from t#e c*r"e! trac/

)eviation tandard # 3 D-30((X4X5 3 (47.(4:.8 5>(4:.6 5> ??..> (49.7 5 3


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Fraph -o * Erequency Table for/!periment in table -o

Table -o ; * Erequency Table for /!periment in table -o 5

Erequency Table

Glass Erequency

040.8

;4;.8 9

:4:.8 :


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,.,. Analysis DataHe use a curved trac1 with 0marble where we release eachmarble from the mar1ed point onthe trac1 0 times. /ach marblemar1 a point in our paper withprecision because all the mar1 arevery close each other.

$t shows the e!perimentcan repeat and reproduce

with precision in the same space.

$n our "rst e!periment where we released 0 marble we found a mean 3 5.


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• $n our "rst e!periment where we released 0 marble we found 5 pointsfelt very near to our mean in the range of our deviation standard. He can"nd a mean in a good range X 3 5.< 9.59. $t shows our e!perimentwas done in the acceptable range (graph -o .

• He observe our points in the paper have good precision because themeasurements of the same quantity are closely cluster and they have

accurate measurement because the measurements are independentmeasurement cluster about the true value.

•

4II References

• )epartment of Physics and Astronomy (/ditionn.,Jniversity Koo1storeGustom Publising, pp. ;48

• )epartment of Physics L Astronomyhttp*@@virgo4physics.sas.upenn.edu@uglabs@labMmanual@/rrorMAnalysis.pdf

• Triola, =ario E. , /lementary tatistics. Tenth /dition. =assuchussets.599

Report 1 Statistical Analysis of Data Phyisc 211 (2)

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