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Randomly Scattered Error Analysis of Data: Lab. Report Measurement

This lab report analyzes error in randomly scattered data. Students recorded the distance traveled by stones thrown at a target line from 2 meters away. The mean, standard deviation, accuracy, and precision were calculated. Data was grouped into intervals and a probability histogram was plotted. The standard deviation was used to estimate the random error based on a 95% probability. Tables show the raw data, intervals, and calculations to analyze the scattered measurements.

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Ahmed El-eraky
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241 views6 pages

Randomly Scattered Error Analysis of Data: Lab. Report Measurement

This lab report analyzes error in randomly scattered data. Students recorded the distance traveled by stones thrown at a target line from 2 meters away. The mean, standard deviation, accuracy, and precision were calculated. Data was grouped into intervals and a probability histogram was plotted. The standard deviation was used to estimate the random error based on a 95% probability. Tables show the raw data, intervals, and calculations to analyze the scattered measurements.

Uploaded by

Ahmed El-eraky
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Ain Shams University

Faculty Of Engineering,
Mechanical Department.

_____________________________________________________________________________________

Measurement Lab. Report

Error Analysis of Randomly Scattered


Data

Presented to: Dr. El-Smanode

Submitted by: Ahmed El-Eraky


2nd. Year Mechanical Department

Table of Contents:

Introduction ...... Page ( 1 )


Objective
.. Page ( 1 )
Procedures
.. Page (1 )
Calculations .. Page ( 2 )
Tables
.. Page ( 3 )
Graphs
.. Page ( 4 )

1.1Introduction:
While conducting any laboratory experiment, a percent of error occurs due to many
factors, the common of them are: human error & random error.
Definition of such an error is important for any engineer while designing a project or
recording readings to derive facts. One of the methods to measure that margin of error is
statistic by calculating the standard deviation.

1.2Objective:
The Experiment is designed to get experimental data sufficient for:
1. Calculating the mean and the standard deviation of a set of measurements.
2. Plot a probability histogram for the data.
3. Estimating accuracy, precision, and the random error of the data based on 95%
probability (significant error) using Gaussian distribution.

1.3Procedures:
Groups of two students are formed to get the measurements as follows:
1. One of the students throws a stone towards a target line drawn on the floor at a fixed
distance of 2 meters from the student, X. The other student will record the distance
traveled by the stone, X.
2. Step one will be repeated for ten times before the two students exchange their places.
3. Collect all data of the groups.
4. Calculate the arithmetic mean of the data, X.
5. Calculate the accuracy and the precision of the readings.
6. Divide the data into intervals of a suitable width.
7. Plot the probability histogram of the data (Z vs. X).
8. Calculate the standard deviation of the readings,
based on the calculated values of X and

and draw the Gaussian distribution

1.4 Calculations:
1) N: number of reading.
2) X: Arithmetic mean.

3) Accuracy =
4) Precision =
5) Probability that a reading will fall in an interval
P=
6) Probability density function, Z=

7) Standard deviation,

X)

1.5 Tables:
N
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30

(m)

2.3
1.8
1.75
1.8
2
1.8
1.75
1.75
2.1
1.75
1.95
1.85
1.9
2
1.85
1.9
2
1.85
1.8
2.05
1.95
2
2.1
1.95
2.15
2
2.2
1.85
2
2.1

X - True Value
0.3
- 0.2
- 0.25
- 0.2
0
-0.2
-0.25
-0.25
0.1
- 0.25
- 0.5
- 0.15
- 0.1
0
- 0.15
- 0.1
0
- 0.15
- 0.2
0.05
- 0.05
0
0.1
- 0.05
- 0.15
0
0.2
- 0.15
0
0.1

X - X
0.36
- 0.14
- 0.19
- 0.14
0.06
- 0.14
- 0.19
- 0.19
0.16
- 0.19
0.01
- 0.09
- 0.04
0.06
- 0.09
- 0.04
0.06
- 0.09
- 0.14
0.11
0.01
0.06
0.16
0.01
0.21
0.06
0.26
- 0.09
0.06
0.16

X)
0.1296
0.0196
0.0361
0.0196
0.0036
0.0196
0.0361
0.0361
0.0256
0.0361
0.0001
0.0081
0.0061
0.0036
0.0081
0.0061
0.0036
0.0081
0.0196
0.0121
0.0001
0.0036
0.025
0.0001
0.0441
0.0036
0.0676
0.0081
0.0036
0.0256

Interval
1.75 ~ 1.8
1.8 ~ 1.85
1.85 ~ 1.9
1.9 ~ 1.95
1.95 ~ 2
2 ~ 2.5

N
8
4
2
3
6
7
30

0.2667
0.1333
0.0667
0.1
0.2
0.2333
1

X
1.75
1.8
1.8
1.85
1.85
1.9
1.9
1.95
1.95
2
2
2.5

Z
5.334
2.666
1.334
2
4
4.666

Z
5.334
5.334
2.666
2.666
1.334
1.334
2
2
4
4
4.666
4.666

1.6 Graphs:

Frequency
9
8
7
6
5
4
3
2
1
0

Frequency

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