Transcript cms/lib04/CA01000848/Centricity/Domain/2671/Section 5.1 Day 2

(Day 2)

In a normal distribution, approximately…
◦ 68% of all data fall within 1 standard deviation of the
mean.
◦ 95% of all data fall within 2 standard deviations of the
mean.
◦ 99.7% of all data fall
within 3 standard
deviations of the
mean.
◦ Remember, the
amount of data will
have an impact on how
close these numbers
are to reality.
34 — 34
13.5
2.35
0.15
13.5
2.35
0.15
1. How much of the data is
greater than 500?
Answer: 50%
2. How much of the data
falls between 400 and 500?
Answer: 34%
3. How much of the data
falls between 200 and 400?
Answer: 50-34-0.15=15.85%
4. How much of the data
falls between 300 and 700?
Answer: 95%
5. How much of the data is
less than 300?
Answer: 100-50-34-13.5=2.5%


What kind of curve is being used if the area
under the curve is defined by a proportion (a
value between 0 and 1).
A DENSITY CURVE
To use the 68-95-99.7 Rule, it also must be
a normal curve.





Symmetric
Bell shaped
Single peak
Tails fall off
No outliers


You can use Chebychev’s Theorem if the
distribution is not bell shaped, or if the shape
is not known.
The portion of any data set lying within “k”
standard deviations (k > 1) of the mean is at
least:
1
1 2
k

If you wanted to know how much data fell
within 3 standard deviations of a data set and
it wasn’t a bell shaped curve or you didn’t
know the shape:
1
1 8
1  2  1    88.9%
3
9 9

This is used to standardize numbers which
may be on different scales.
z
x

x  non  standardized
z  standardized
  mean
  standard _ deviation


Answer can be between -3.49 and +3.49.
Z-scores represent the number of standard
deviations above or below the mean the
number is.
◦ If z=1, the value is 1 standard deviation above the
mean.
◦ If z=-2, the value is 2 standard deviations below
the mean.




During the 2003 regular season, the Kansas City
Chiefs (NFL) scored 63 touchdowns. During the
2003 regular season the Tampa Bay Storm (Arena
Football) scored 119 touchdowns. The mean
number of touchdowns for Kansas City is 37.4
with a standard deviation of 9.3. The mean
number of touchdowns for Tampa Bay is 111.7
with a standard deviation of 17.3.
Find the z-score for each.
KC = 2.75
TB = 0.42
Kansas City had a better record of touchdowns
for the season (much higher above the mean).

Cth percentile of a distribution is a value such
that C percent of the observations lie below it
and the rest lie above it.
◦ 80th percentile =
 80% below, 20% above = Top 20%
◦ 90th percentile =
 90% below, 10% above = Top 10%
◦ 99th percentile =
 99% below, 1% above = Top 1%
 Pg.
297..306
◦#7-14, 16-18, 25, 27

Important Notes
◦ For the window settings, the two numbers in the brackets
represent the minimum and maximum; the subscript
number represents the scale.
◦ Add in the age for President Obama: 47 years old.
◦ Question 4 now changes to 44 data points since we have
now included President Obama in the data.
◦ In order to sort the L1 list into L2 and L3, highlight the L2
and L3 headings and type in L1. This will copy the data
into each column. To sort L2 in ascending order hit STAT,
#2, L2; to sort L3 in descending order hit STAT, #3, L3.
◦ Add these 2 questions:
 What percent are age 42.32 years – 60.80 years? How does this
compare with what should happen with the 68-95-99.7 rule?
 What percent are below age 59.64 years? How does this
compare with what should happen with the 68-95-99.7 rule?