#### Transforming Data

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Transforming Data

Transforming Data
Let’s look at our test data!
Transforming Data
Transforming converts the original
observations from the original units of
measurements to another scale.
Transformations can affect the shape,
center, and spread of a distribution.
What effect does adding have on
the data?
Effect of Adding (or Subtracting)
a Constant
Adding the same number a (either
positive, zeros, or negative) to each
observation
Adds
a to measures of center &
position(mean, median, percentiles, but
Does not change the shape of the distribution
or measures of spread (range, IQR, standard
deviation).
What if I multiplied everything by 10?
Original Data
1
2
3
4
5
Effect of Multiplying (or Dividing)
by a Constant)
Multiplying (or dividing) each
observation by the same number b
(positive, negative, or zero).
Multiplies
measures of center and location
9mean, median, quartiles, percentiles) by b
Multiplies measures of spread (range, IQR,
Standard deviation) by |b|, but
Does not change the shape of the
distribution.
So… our last test scores. Change to a z-score:
Original data has a mean of 50 and
standard deviation of 5….
What happens to both if we add 20 to
each item?
What happen to both is we multiply 20 to
each item?
Density Curves
Weight of newborns
Nearest pound
4
5
6
7
8
9
Nearest tenth of pound
4
5
6
7
8
9
Fit more & more rectangles
It approaches a curve as the rectangles
become smaller & has greater accuracy.
Density Function
•
Describes the overall pattern of a distribution.
•
The area under the curve and above any interval
of values on the horizontal axis is the proportion
of all observations that fall in that interval.
•
The graph is a smooth curve called the density
curve.
•
Total area under the curve = 1.
Uniform Distribution
All occur in equal distributions
Ex:
.5 if 4 x 6
f ( x)
0 otherwise
What’s the area from 4.5 to 5.5?
What’s the area from 5.5 to 6?
If we have a uniform continuous
function from 3 to 8, find the
height.
Ex.
0.02
50 minutes
Find P(x < 10)
Find P(x < 35)
0.25
Ex:
Find P(x<4)
Find P(x<2)
0.02
Ex:
50
Find P(x<20)
Find P(x>70)
Find P(20<x<70)
100
Homework
Page 107(19, 21, 23, 25)
Worksheet