Dear Student,
Please find attached your summer review packet for Introduction to Statistics. The
problems in this packet are designed to refresh your familiarity with the graphing
calculator which is required for the course. If you need review, you can use the
attached websites for additional information. Internet access is available at all public
libraries.
The packet is due the first day of class, and will be graded. To receive full credit, you
will need to complete all parts and show all work as necessary/appropriate. This
assignment will count toward your first quarter grade and your first quiz of the year will
be on this material. Don’t wait until the last minute!!
If you have any questions please do not hesitate to contact the High School at: 860844-3014 or you can email Mr. Coxon after August 25th at: coxonl@granby.k12.ct.us
We are looking forward to seeing you on the first day of school!
- The Math Team at GMHS
Below is a list of topics covered in the packet with formulas and helpful websites:
Integers (Adding, Subtracting, Multiplying, Dividing)
http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=signed
Rules of Divisibility
http://www.mathgoodies.com/lessons/vol3/divisibility.html
http://www.mathsisfun.com/divisibility-rules.html
Rational Numbers (Ratios & Proportions, Fractions, Decimals, Percentage)
http://regentsprep.org/Regents/math/rational/Lrat.htm
http://www.purplemath.com/modules/ratio.htm
http://www.purplemath.com/modules/percents.htm
http://www.purplemath.com/modules/fraction.htm
http://www.visualfractions.com/
http://www.mathsisfun.com/converting-decimals-percents.html
http://www.mccc.edu/~kelld/CompFDP.htm
Order of Operations
http://www.mathgoodies.com/lessons/vol7/order_operations.html
http://www.purplemath.com/modules/orderops.htm
The Distributive Property
http://www.purplemath.com/modules/numbprop.htm
http://www.freemathhelp.com/distributive-property.html
Translating Algebraic Expressions
http://www.purplemath.com/modules/translat.htm
http://www.mathgoodies.com/lessons/vol7/equations.html
Evaluating Algebraic Expressions
http://www.purplemath.com/modules/evaluate.htm
http://regentsprep.org/Regents/math/orderop/evalPrac.htm
Solving One-Step Equations and simple Two-Step Equations
http://www.purplemath.com/modules/solvelin.htm
http://regentsprep.org/Regents/math/solveq/LSolvEq.htm
Graphing points (coordinates) on a Coordinate System (Cartesian Plane)
http://mathforum.org/cgraph/cplane/pexample.html
http://www.math.com/school/subject2/lessons/S2U4L1GL.html
atistics
Intro To Sta
Sum
mmer Pa
acket
Name:__
__________
________
N
The Intro Stats
s Summer Packet
P
is de
esigned witth the TI-84
4 model of G
Graphing
Please Note:
Calculattor in mind. The TI-83
3 model is very
v
similar and should
d be fine. H
However, th
he
Summerr Packet is not designe
ed to work with other b
brands of ccalculators tthat do not have the
same menus and fe
eatures.
f
all dirrections and complete
e the assign
ned tasks a
and question
ns. All que
estions
Please follow
must be completed
d with work shown as appropriate
a
e. This Sum
mmer Packe
et will be grraded.
Task #1)
# Sum
mmary Statistics
S
s
In this tu
utorial, we will
w focus on
n entering a set of datta to calcula
ate important bits of in
nformation
easily on
n the calcullator. Throughout this
s class, hop
pefully you w
will see tha
at your grap
phing
calculato
or is a grea
at tool and resource
r
tha
at can do w
way more th
han simple calculations.
oblem, we will
w be takin
ng a sample
e of informa
ation and calculating the mean
For this specific pro
e), standard
d deviation, and differe
ent quartile
es. Please follow the ssteps carefu
ully ☺
(average
Suppose
e we wished to see wh
hat the average length
h of a blade
e of grass iss here in Grranby, CT.
We go outside
o
and pluck 16 blades
b
and carefully
c
m easure the length of e
each in centimeters.
Here are
e the results:
4
7
5
4
Length of
o Grass Blades (cm))
8
3
7
10
6
6
8
5
4
3
2
4
This set of data is called
c
a ‘Sa
ample’ whic
ch is just ass it sounds. It’s a piece
e, or samplle, of the
entire po
opulation off grass blad
des in Gran
nby.
Now, lett’s use the calculator
c
to
o find out some
s
inform
mation abou
ut this set o
of data.
Step 1: Push on th
he [ON] buttton on your calculatorr and make
e sure you h
have a set o
of flashing
pixels on your “home screen.” This is where you are typically used
d to doing m
most of
your work on
n these calc
culators. In
n stats we w
will be bran
nching out a
away from tthis.
Step 2: Press the [STAT] buttton (hmm…
…Statistics course….) and your sscreen shou
uld look
lik
ke this:
Notice
N
all the
e submenu
us on the top of the scrreen. We h
have “EDIT
T”, “CALC”, and
“T
TESTS.” We
W will be using all of these
t
option
ns at some
e point over the course
e of the
year. Please feel free to
t get yours
self acquain
nted with th
he different menus. Y
You can
use the arrow buttons to
t move aro
ound these sreens.
Step 3: On the me
enu “EDIT” which
w
by de
efault come
es up first, h
highlight Op
ption “1: Ed
dit” and hit
[E
ENTER]. Your
Y
screen
n should no
ow look like this: (it’s okay if it doe
esn’t say “R
RESID” ☺)
Step 4: This is the place in yo
our calculattor where yo
er in sets o
of data like w
we
ou can ente
collected above (the bla
ades of gra
ass). If you use the arrrow keys to
o move up tto
1” or “L2” ettc., you can
n press the [CLEAR] b
button to wiipe out the list and
highlight “L1
make
m
it free for typing in new data
a. Practice typing in so
ome random
m numberss and
clearing it ou
ut afterward
d. This is merely
m
to ge
et familiar w
with the sysstem.
e sample data in the ta
able from th
he front pag
ge. You sh
hould have
Step 5: Using “L1”, type in the
a total of 16 pieces of data.
d
After you are do
one with thiss, please do
o the follow
wing key
command:
Hit
H the butto
on [STAT], move over to “CALC””, then choo
ose the opttion “1: 1-V
Var Stats”.
Your
Y
screen
n should cha
ange to loo
ok like this:
p all of ou
ur data into “L1”, presss [2ND]
[1
1] which willl be choosing choice
Step 6: Since we put
L1. Now hit enter to ge
et a screen as follows.. *note – m
my numbers
s/answers are
different
d
tha
an what yo
ou will get ☺ I can’t d
do the worrk for you!*
Step 7: You can scroll down using the arrow keys to get information that is not shown due to
the small screen size. Please fill in the following information:
x=
Sx =
σx =
n=
min X =
Q1=
Med =
Q3=
MaxX =
Are any of these values/variables something that you already knew?? Explain which ones.
Question 1: The average of our data corresponds to the symbol x (read, x-bar). Using this
data, what is the average length blade of grass in our sample we took?
Question 2: ‘Sx’ represents the spread of our data (how far away data is from the average
we found). In general, 99.7% of the data is between ±3 ‘Sx’ away.
Does this hold true with your data? In other words, if I add and subtract 3 of the ‘Sx’ form the
average found in question 1, does this range encompass all of our data?
Questio
on 3: This next
n
one is easy. ‘n’ represents
r
tthe numberr of pieces of data that we
collected
d. How ma
any pieces of
o data did we use in tthis mini-stu
udy?
Questio
on 4: The Median
M
of th
he data is found
f
by rea
arranging e
every value
e in order an
nd finding
the midd
dle term. The
T calculattor calculate
es this for u
us. Please locate wha
at you found
d for ‘Med”
and write your answ
wer.
Task #2)
# Gra
aph a His
stogram
m (simila
ar to a ba
ar graph
h).
Step 1:
Turn the Calcula
ator On.
P
Press [ON]
Step 2:
Clearr the screen
n.
P
Press [Clea
ar]
Step 3:
Go to
o menu nee
eded to ente
er data.
P
Press [STA
AT]
Step 4:
You should
s
now
w see 3 subm
menus acro
oss the top of the scre
een:
ED
DIT
CALC
TESTS
Under the first drop-down men
nu called ED
DIT, you sh
hould see 5 options.
We wantt the first op
ption called “1:Edit…”
Choose “1:Edit”
“
by moving cursor onto th
hat choice, and Press [ENTER]
Step 5:
You shou
uld now see
e 3 columns on the sccreen with tthe names o
of those co
olumns
(lists)) as “L1,” “L
L2,” and “L3
3.”
If you
u move your cursor to the right, offf the edge
of the
e screen, yo
ou will see there
t
are m
more lists th
hat go up to
o list “L6.”
These
e lists are where
w
we enter
e
data in
nto the calcculator.
Step 6:
Enter the following raw data in
nto the calcculator:
Number of
o times Ga
ary the snai l is observe
ed “meowin
ng”
in a rando
omly selectted Sponge
eBob episod
de.
2
3
1
0
5
1
2
2
3
4
4
3
Move
e your curso
or to the top
p of the colu
umn titled ““L1.”
Then, move dow
wn to the firrst space (ccalled a “cell”) beneath
h the “L1” space.
Enterr the first nu
umber in the
e table.
Press
s [Enter] orr the down arrow.
Enterr the next number. Etc
c…
Continue until alll of the num
mbers are e
entered.
Step 7:
Quit out to
t a home screen.
s
To do this, pre
ess [2ND]:[Q
QUIT] (Qu
uit is really tthe
[M
MODE] butto
on right nexxt to the [2NND] button).
Step 8:
Go to the
e menu to set up the histogram.
Press
s [2ND]:[STA
AT PLOT]
([STAT PLOT] is re
eally the [Y
Y=] button
right above the [2NND] button)
s
see a menu tha
at looks like
e the follow
wing:
You should
e is space to
t set up an
nd store 3 d
different gra
aphs in the graphing calculator
There
underr options 1,, 2, and 3 th
hat you see
e on this screen.
(Y
You should
d only have either no graph
g
plots currently on
n, or only o
one graph p
plot on at
th
his time. If you have more
m
than one
o graph ccurrently on
n, choose o
option 4 to turn off all
graphs,
g
whic
ch takes yo
ou back to th
he home sccreen, and then come
e back into tthis menu.)
If you
u have no plots
p
currenttly on, choo
ose plot opttion 1. If yo
ou have one
e plot
currently on, cho
oose that plot option.
You should
s
see a menu tha
at looks like
e the follow
wing graph ((see next pa
age):
ord “On” and
d press [En
nter].
Highlight the wo
Move
e your curso
or down to the
t next row
w titled “Tyype.”
Move
e your curso
or to the right until you
u highlight the 3rd graph option tha
at looks
like a bar graph (it’s not, it’s
s a histogra
am), and prress [Enterr] to select tthat plot
type.
Move
e your curso
or down to the
t row title
ed “Xlist.” It should sa
ay “L1” nextt to the
“Xlist:”
If it do
oes not, change it to “L1” by movving your cu
ursor onto tthe list curre
ently
name
ed there and
d enter [2NDD]:[L1]
(([L1] is reallly the [1] button)
Move
e your curso
or down to the
t last row
w titled “Fre
eq:” It shou
uld have the
e number
“1” en
ntered there
e. If it does
s not, enter a “1” after the “Freq:”
Step 9:
k to the hom
me screen.
Press [2ND]:[QUIT] to go back
utton in the
e top centerr of the calcculator.
Then, press the [ZOOM] bu
s
see a menu tha
at looks like
e the follow
wing:
You should
Choo
ose option #9,
# called “Z
ZoomStat”
You should
s
now
w see a histo
ogram, whicch looks likke a bar gra
aph, but without
space
es in betwe
een the bars
s, and pure
ely numerica
al data.
Step 10: Press the
e [TRACE]] button in the upper right of the ccalculator, a
above the ffour
direction
nal arrow bu
uttons.
As yo
ou press lefft or right, you should ssee at the b
bottom left of the scree
en a
descrription of the number range
r
each bar repressents (i.e. w
what types o
of numbers
went into that ba
ar). At the bottom
b
righ
ht of the scrreen you sh
hould see a statement
that says
s
n=#. This
T
numbe
er tells you how many pieces of d
data fell in this bar.
Use this
t
informa
ation on this
s screen, to
o copy the g
graph accurrately onto the blank
graph
h below.
4
3
2
1
0
0 to <1
1 to <2
2 to <3
3 to <4
4 to <5
5 to <6
Task #3)
#
Sim
mulate ro
olling a regular 6-sided
d die.
Step 1:
Turn the Calcula
ator On.
Presss [ON]
Step 2:
e sure you are
a on the home
h
scree
en. If not, ..
Make
Presss [2nd]:[Qu
uit]
Step 3:
Clearr the screen
n.
Presss [Clear]
Step 4:
Go to
o the menu that has the command
d to genera
ate a random integer. We will
use th
his command to rando
omly genera
ate numberrs from 1 th
hrough 6, to
o simulate
rolling
g a single die.
d
Press
s [MATH] button.
b
Move
e over to the
e PRB drop
p-down men
nu
Choo
ose option 5,
5 “5:randInt(”
Step 5:
This command should now be sitting on your homescreen waiting for you to
continue.
The command requires some information to generate the numbers that we want.
Let’s generate one single random roll of our die.
Enter the following numbers after the command so that your command looks like
the following:
5:randInt(1,6)
and then press [ENTER]
Write the number that you just “rolled” on your simulated die
=> ___________
Now,… press [ENTER] again, to roll another die.
Write the number that you just “rolled” on your simulated die
=> ___________
And…. One more time…. Press [ENTER] again to roll a 3rd die.
Write the number that you just “rolled” on your simulated die
=> ___________
Step 6: We can also roll several die rolls with one command, without having to hit [ENTER]
over and over. We will run the same command again, but this time we will enter a third
number. We will tell the command to roll the die 5 times.
Again,
Press [MATH] button.
Move over to the PRB drop-down menu
Choose option 5, “5:randInt(”
Then, enter the following numbers so that your command looks like this…
5:randInt(1,6,5)
and then press [ENTER]
Write the 5 numbers that you just “rolled” on your simulated die
=>
_________
_________
_________
_________
_________
These have been a few examples of some very commonly used
menus and capabilities of the TI-Graphing calculator that will be
used extensively in this course.
You are now Done with the Packet!!! ☺