Transcript 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
