Statistical Reasoning
for everyday life
Intro to Probability and
Statistics
Mr. Spering – Room 113
2.2 Dealing with Errors

Random Errors – occur because of random and
inherently unpredictable events in the measurement
process. Random errors can not be corrected.
However, they can be minimized by making many
measurements and find the mean. (i.e. measuring the
decibels of a band, at a concert)

Systematic Errors – occur when there is a problem in the
measurement system. Systematic errors can be
corrected if they are discovered. (i.e. A scale is 2 pounds
heavy →calibration error)
---A little inaccuracy sometimes saves a ton of explanation---
2.2 Dealing with Errors


Absolute Error – describes how far a measured value lies from the
actual value; it is the difference between the measured value and
the actual: (Usually state as absolute value, but the sign signifies
too high or too low)
absolute error = measured value – actual value
Relative Error – compares absolute error to the size of the actual
value and can be expressed as a percentage:
relative error = measured value – actual value X 100%
actual value
2.2 Dealing with Errors

Examples:
Absolute error: I am driving 57 mph and radar
measures my speed at 53 mph.
53  57  4
Relative error: I weigh 230 pounds but the scale
reads 225.
225  230
 100%  2%
230
2.2 Dealing with Errors



Accuracy vs. Precision:
Accuracy – describes how closely a
measurement matches an actual value. An
accurate measurement is very close to the
actual value. (i.e. Measure an angle at 73
degrees, actual angle is 73.3 degrees)
Precision – describes the amount of detail in a
measurement (i.e. The cows produced 949.54
gallons of milk is more precise than the cows
produced 950 gallons of milk.)
2.2 Dealing with Errors
2.2 Dealing with Errors

Find the absolute and relative error for each situation:
Your actual weight is 200 lbs and the scale reads 202 lbs.
Absolute: too high by 2 lbs
Relative: too high by 1%
The government claims that a program costs $99 billion, but an audit
finds that it actually cost $100 billion.
Absolute: too low $1 billion
Relative: too low by 1%
You’re building a deck. You figure you need 180 sq ft of decking to
complete the deck. You actual need 150 sq ft.
Absolute: too high 30 sq ft
Relative: too high 20%
2.2 Dealing with Errors

Accuracy and Precision:
Suppose that you actually weigh 115.4 pounds. The scale at the
doctor’s office, which can be read only to the nearest quarter pound,
says that you weigh 115 ¼ pounds. The scale at the gym, which gives
a digital readout to the nearest 0.1 pound, reads 119.7 pounds. Which
scale is more accurate? Which is more precise?
The scale at the doctor’s is more accurate. The scale at the gym
is more precise.
When studying tax brackets, your income is $51,000, one bracket
measures in thousands of dollars the other in hundreds of dollars.
Which is more precise?
The bracket measured in hundreds of dollars is more precise.
Two censuses are conducted one says your hometown has 4000
people the other claims there are 6000 people. Which census is more
accurate?
Equally accurate
2.2 Dealing with Errors
 Summary:
 Errors
can occur in many ways, but generally two types:
random errors and systematic errors

Random errors are errors resulting from random mistakes in
reading, recording, and evaluating data.
 Whatever
the source of an error, it can be described in
two different ways: absolute or relative
 Once a measurement is reported, we can evaluate it in
terms of its accuracy and its precision
----Mistakes are the portals of discovery--James Joyce
2.2 Dealing with Errors
 Homework

#6:
Pg 65 # 5-19 and 27-37 odd
--A man of genius makes no mistakes.
His errors are volitional and are the portals of discovery.--