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TAKS Tutorial
Objectives 5 & 9
part 1
If you wish to go back over this lesson…
or view any lesson from a previous
session that you might have missed
or just wish to review again…
Please go to the Spring High webpage
and click on the link for math
tutorials or
visit Mrs. Nelson’s webpage
Objective 9 on Probability & Statistics
is tested at all levels of TAKS
Today, we will work with:
 Central measures of tendency
(mean, median, mode, range)
 Compound probability
Let’s start with MEDIAN
Median is the value that is in the
middle of a data set.
Let’s see a visual depiction of median.
X
X
X
X
X
X
Place the buildings in order by height.
Now, eliminate a smallest and a largest building until you
get to the middle. MEDIAN --MIDDLE
On the TAKS test, you will be given a
set of numbers in a data set.
The first thing you want to do is to put
those numbers in numerical order
from smallest to largest.
Then, just like we did with the
buildings, you want to cross out one
smallest and one largest number IN
PAIRS until you get to the middle.
What happens if you have nothing left
after eliminating the pairs?
Use the last pair, the two middle values, and find their
average. You want the number in the middle of them.
Let’s move on to MODE
Mode is the value that occurs most
often in a data set.
Let’s see a visual depiction of mode.
Tally how many times each height occurs.
All of the buildings are tallied. The height that
occurred most often is 180 meters.
There are some facts you need to
remember about Mode.



The value must occur more than
once to be a mode
If all values occur only once, there
is no mode.
If more than one value occurs most
often, each are modes.
RANGE is the difference between the
largest and the smallest data value.
With your data in order from smallest
to largest, just subtract.
Largest value – smallest value = Range
The MEAN (or AVERAGE) value is where
we “play fair” and act like Robin Hood.
We take from the largest values and
give to the smallest values so they
all have an equal amounts.
This process is what happens to your
grades—we take points from your
highest grades to give to your
lowest grades until we get equality.
That is why zeroes hurt your grade
so much!
We need to look for a value where each of
these buildings would be equal in height.
How about right here?
This
extra
Could
go
here
We need to look for a value where each of
these buildings would be equal in height.
How about right here?
This
extra
Could
go
here
We need to look for a value where each of
these buildings would be equal in height.
How about right here?
The
extra
Could
go
here
And
here
We need to look for a value where each of
these buildings would be equal in height.
Right here looks just fine!
-30m
-20m
+30m
-30m
+40m
+20m
-10m
150 m
150 m
150 m
150 m
150 m
150 m
150 m
It is much easier to find the MEAN by just
adding all the data values together and
then dividing by the number of values.
Then, you don’t have to figure out
how to divide everything up evenly.
The process does it automatically.
This problem was on the April 2006 test.
You can see that having all 4 measures as
options requires you to know them all and
perform them all.
Task 1:Put the car prices in order from least
to greatest. Fortunately for us, they already
are in that order.
So now,
bring out the
calculator
and find the
mean.
$863
$750
$995
Lightly cross out the smallest
& largest values in pairs to
find the median.
$895
The number there most often is $995 so that is
the Mode.
Range: 1495 – 600 = 895
In Middle School, you learned to find
simple probability. You then extended
that knowledge to compound probability.
Compound probability is where you
find the likelihood of one event
happening and multiply it by the
likelihood of the next event
happening.
For instance, you just dumped all of
you clean socks in your sock drawer
without folding them. One morning
before school, you get dressed in the
dark. What is the probability that when
you pull one sock out of the drawer, put
it on your foot, and then pull out a
second sock and put it on your other
foot, that you have the same color
socks on your feet?
Before we can answer this question, we
need to know how many socks we have of
each color.



If we only have one color of socks—
say they are all black—the
probability of having the same color
socks on our feet is 1. We definitely
have a matched pair!
If every sock in the drawer is a
different color, then the probability
of a matched pair is 0.
All other probabilities are some
fractional value between 0 and 1.
Let’s say we have 8 black socks, 4
brown socks, 6 white socks, and 4
blue socks in our drawer.
What is the probability that we have a
pair of black socks on our feet?
It would mean that we would have
had 8 chances out of 22 total socks
to get a black sock the first time.
8
22
Remember, that sock goes on our
foot, so now we have 21 socks in
the drawer. I have 1 of the black
socks on my foot, so there are 7
black socks left out of the 21 socks
still in the drawer.
7
21
To find the probability that I have the
pair of black socks on my feet, I
need to multiply the two single
probabilities together.
Since most of you don’t like fractions
anyway, let your calculator do the
multiplying for you. Just remember to
put parentheses around your fractions!
We have only a
4 in 33 chance
of having a
matched pair of
socks. Not very
good odds!
We do NOT want that decimal. So, use the
calculator again to convert the probability
into a fraction. Remember, MATH Frac
This question was on the 2004 test.
Although Jamal’s name is 5
letters long, there are only 4
different letters used. He has a
4 out of 26 probability of
drawing a letter from his name.
4
26
This question was on the 2004 test.
Half of the number tiles are odd
and half of them are even.
There are 5 out of 10 odd
numbers: 1, 3, 5, 7. and 9.
5
10
This question was on the 2004 test.
Multiply the probability of each
event happening.
Today, we are also going to take a look
at Objective 5 Non-linear Functions
Since this test covers Algebra I
material, we are talking about
Quadratic Functions and a small
amount on Exponential Functions.
That doesn’t mean that you won’t see
other functions that you have
studied mentioned in the test
questions.
With respect to the quadratic functions:
Today, we will work with:
 Parameter changes on the parent
function, y=x2 (which is part of
Objective 2)
 Comparing the graphs of any 2
quadratic functions
 Solving quadratic equations
 Roots, solutions, zeroes, x-intercepts
In Objective 2, the expectation is that you
know the equation of the linear and quadratic
parent functions…
In Objective 5, the expectation is that you will
know the effect that changes on the parent
function will have on its graph.






y = x2
y = ax2 + c
Translation: up when c is positive
Translation: down when c is negative
Reflection: when a is negative
Dilation: wider when a is smaller than 1
Dilation: narrower when a is larger than 1
2006 test
You may only translate
up or down. Look at
the graph you have.
Find where x = 6.
Now, find the point
(6, 7)
4
4
To get from the point
on the given graph
(6, 11) to the point
(6, 7), you need to
translate down 4 units.
If the entire graph
moves down 4
units, the new yintercept/vertex is
at (0, -5)
Now, look at the answer choices.
Which function has the correct y-intercept? (Also,
note that two of the functions open downward
because the 1/3 is negative. Our graph opens
upward.)
To check your
answer, enter
the function in
the calculator
and consult
the table to
make sure
(6, 7) is there.
2006 test
Analyze the first function. The
coefficient is negative—so the
graph opens downward.
¾ is a number smaller
than 1 so that parabola is
wider than the parent.
4/3 is a number larger
than 1 so that parabola is
narrower than the parent.
Consequently, the ¾ makes the first parabola wider than 4/3.
A big MUST to remember…
These expressions/words all mean the
same thing!!!!
 roots
 solutions
 zeroes
 x-intercepts
Know this information!!!!!!!
2006 test
If you know that roots are xintercepts, you just need to look
at the graph to find where the
parabola crosses the x-axis.
All x-intercepts have
zero for a y-coordinate!!
Between
2 and 3
Between
6 and 7
2003 test
Move 36 to
the left
side of the
equation
(= 0
“zeroes”)
and enter
in y1 on the
calculator.
You have several options
for solving this problem!
Option 1: solve
graphically, finding the
x-intercepts
2003 test
Adjust the window—you
don’t need that much of
the x-axis.
You can approximate
the x-intercepts.
About
-1/3
About
5/3
2003 test
This option
is the only
one with
-1/3
If you don’t
like these
fractions, you
can change
them all to
decimals.
Adjust the window—you
don’t need that much of
the x-axis.
Or you can CALC the
zero
Just to show you
the other solution…
-.33333
is
1.66666…
-1/3
is 1 2/3
which is
5/3
About
-1/3
About
5/3
Here is another option…
2003 test
Use
Enterthe
theCALC
left
feature
and
side of the
find
the in y1
equation
intersect(ion)
and the right
side in y2. You
will need to
adjust the
window so
ymax is higher
than 36.
Option 2: solve
graphically, finding the
intersection.
Once again,
-.33333 is
-1/3 and C is
the only
option with
that
solution.
2003 test
And a third option! Solve
Algebraically
4(3 x  2)  36
Divide both sides by 4
(3x - 2)  9
Square root both sides
2
2
(3x - 2)  9 Simplify
2
3x - 2   3 Split into 2 problems
Using the 
Using the 3x - 2  3
3x  5
x
5
3
3x - 2  - 3 Add 2 to each side
3x  - 1 Divide each side by 3
x 
1
3
More Practice for these topics…

Here are some problems for you to
do…
11’03 8 An automobile dealer is analyzing
a frequency table identifying the number of
vehicles of each color sold during the last 6
months. Which measure of data describes
the most popular color of vehicle sold?
F
G
H
J
Mean
Median
Mode
Range
10’04 34 Nicholas earned the following
grades on his science exams: 83, 88, 87,
and 83. If Nicholas scores a 90 on his last
exam, which measure of central tendency
will give him the highest score?
F Mode
G Median
H Range
J Mean