Download 15% .15%

Statistical Analysis on the TI-84
Finding the mean, median, standard
deviation, range and mode of a set of data.
Press the STAT button, and select EDIT
Now, enter the following numbers into
L1.
5,10,7,5,8,9,10,12,15,17,13,12
Statistical Analysis on the TI-84
Once the numbers have been entered, go to STAT
again.
Select STAT, then arrow to CALC, enter 1, then
press Enter 3 times
This calculates 1-variable stats
You will see the following information:
𝑥 = 10.25 (this is the mean)
∑x = 123 (this is the sum of our list)
∑x2 = 1415 (we won’t use this)
sx = 3.744693215 (stan. dev. of a sample)
σx = 3.585270794 (stan. dev. of a population)
Statistical Analysis on the TI-84
n = 12 (number of items – sample space)
Arrow down for more info!!
Min X = 5 (smallest value)
Q1 (median of top half of data)
Med = 10 (median of all data)
Q3 (median of bottom half of data)
Max X = 17 (largest value)
To find the range, simply subtract Min X from
Max X
(in our case, 17 - 5 = 12)
Statistical Analysis on the TI-84
The values that we will use for now are:
𝑥 = 10.25
σx = 3.58 (rounded)
MinX = 5
MaxX = 17
Statistical Analysis on the TI-84
If you are going to need to find the mode, you
would want to sort the data.
STAT - 2 gets you to the SORT A function.
Type in 2nd 1 (to sort L1) and press Enter
It will say DONE.
This will put the numbers into ascending
order.
STAT - 3 does the same thing, only in descending
order.
Apply to a Normal Distribution
Applying this data to a normal distribution
Also called a bell curve.
2.77
6.51
-3.74
10.25
-3.74
13.99
17.73
+ 3.74
+ 3.74
Standard Deviation Gap:
Distance between each line from the mean
Apply to a Normal Distribution
Percentages that hold for ALL normal
distributions.
34.1%
2.15%
13.6%
34.1%
13.6%
2.15%
68.2% of data occurs between -1 and 1 s.d.
95.4% of data occurs between -2 and 2 s.d.
99.7% of data occurs between -3 and 3 s.d.
𝑥−𝜇
𝑧=
𝜎
Apply to a Normal Distribution
Z-Scores
Used when we want to find the
percentage of data above or below
numbers that do not fall exactly
on a standard deviation line.
The number we are interested in
minus the mean divided by the
standard deviation.
Normal Distribution
The heights of adult American males are
normally distributed with a mean of 69.5
inches and a standard deviation of 2.5 inches.
What percent of adult American males
are between 67 and 74.5 inches tall?
What are the z-scores?
(67-69.5)/2.5 and (74.5-69.5)/2.5
-1 and 2
What percentage of data points lie
between -1 and 2 standard deviations?
34.1 + 34.1 +
13.6 = 81.8%
μ = 69.5
σ = 2.5
64.5
.15%
67.0
69.5
72.0
74.5
.15%
Normal Distribution
In a group of 2000, about how many would
you expect to be taller than 6 feet (72
inches)?
What is the z-score?
(72-69.5)/2.5 = ?
z-score is 1.
What percentage of data points will lie
above 1 standard deviation from the
mean?
13.6 + 2.15+.15
= 15.90%
μ = 69.5
σ = 2.5
64.5
.15%
67.0
69.5
72.0
74.5
.15%
Normal Distribution
In a group of 2000, about how many would
you expect to be taller than 6 feet (72
inches)?
Notice that the question doesn’t ask for
the percentage, it asks for the number of
men out of a group of 2000.
We would take the 2000 times the
percentage to get our guess.
2000*.159 = 318
Normal Distribution
Josh’s and Richard’s Algebra II grades for the
third cycle have the same mean (70). But
Josh’s standard deviation is 15.6, and
Richard’s is 20.1. What does the data tell us
about their grades?
Richard σ = 20.1
29.8
38.8
49.9 70
54.4 70
Josh σ = 15.6
90.1
85.6
110.2
101.2
Josh was more consistent; Richard less so
Using the Calculator: Example 1:
The weights of newborn humans are normally
distributed about the mean, 3250 grams. The
standard deviation is 500 grams.
Find the probability that a baby chosen at
random weighs between 2250 and 4250
grams.
3250
2250
4250
95.4% of babies will be in the given range.
Using the Calculator: Example 1:
2nd VARS 2 –
Lower number = 2250
Upper number = 4250
Mean = 3250
S = 500
p = 0.954
Example 2:
A company manufactures batteries having a
lifespan that are normally distributed with a
mean of 45 months and a standard deviation
of 5 months.
Find the probability that a battery chosen at
random will have a lifespan of 50-55 months.
Step 1: Find the lower and upper z-scores.
50−45 55−45
,
5
5
The z-scores are 1 and 2.
45
50
55
13.6% chance that the battery will have a
lifespan between 50-55 months.
Using the Calculator: Example 2:
2nd VARS 2 –
Lower number = 50
Upper number = 55
Mean = 45
S= 5
p = 0.136
Stat – Edit – Enter numbers into L1
Stat – Calc – 1-Var stats
Mean is 9.46
Standard Deviation (population) is 3.74
Mean is 9.46
Standard Deviation (population) is 3.74
Based on these numbers, how likely is it that
the next snowfall of more than 6 inches is
between 10 and 15 inches?
2nd VARS - 2
Lower - 10
Upper - 15
Mean - 9.46
s = 3.74
p = .373, or 37.3% chance
Today's Assignment:
Pages 737-738; #7-28 and 30-31 (Skip 29)