Let’s look at our test 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
Effect of Adding (or Subtracting)
Adding the same number a (either
positive, zeros, or negative) to each
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
What if I multiplied everything by 10?
Effect of Multiplying (or Dividing)
by a Constant)
Multiplying (or dividing) each
observation by the same number b
(positive, negative, or zero).
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
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
What happen to both is we multiply 20 to
Weight of newborns
Nearest tenth of pound
Fit more & more rectangles
It approaches a curve as the rectangles
become smaller & has greater accuracy.
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
Total area under the curve = 1.
All occur in equal distributions
.5 if 4 x 6
f ( x)
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
Find P(x < 10)
Find P(x < 35)
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