Data Management
&
Analysis
Topics:
• Session 1: Basic Formulas and Data
Presentation
• Session 2: Table, Charts, Graphs and
Coordinate Grids
• Session 3: Basic Statistics
Mathematics
• Mathematics is the science that deals
with the logic of shape, quantity and
arrangement. Math is all around us, in
everything we do. It is the building block
for everything in our daily lives, including
mobile devices, architecture (ancient and
modern), art, money, engineering, and
even sports.
CSC Exam Statistics
Basic Tips:
• Be familiarize with the basic
conversion (Metric System)
• Basic Formulas
Metric System
Metric System
Basic Geometric Formulas
Basic Geometric Formulas
Session 1: Objectives
• Identify and apply the correct formula for a
given situation;
• Solve for any unknown component of the
formulas for perimeter, circumference, and area
of regular and irregular shapes, and volume;
• Use the Pythagorean Theorem in the context of
real-life situations; and
• Demonstrate techniques and choosing best
format to display data.
Sample Problem 1
• A community member
has donated a small lot
to be used as a parking
lot for a public library
and recreation center.
The figure below shows
the dimensions of the
lot.
Sample Problem 1
• Which of the following
expressions can be used
to find the length of side
x?
(1) 50 x 3
(2) 50 + 602
(3) 602
(4) 70 + 60
(5) 60 + 60 + 50
Sample Problem 1
• Which of the following
expressions can be used
to find the length of side
x?
(1) 50 x 3
(2) 50 + 602
(3) 602
(4) 70 + 60
(5) 60 + 60 + 50
Sample Problem 2
• What is the perimeter of
the parking lot in yards?
(1) 600
(2) 540
(3) 470
(4) 430
(5) 300
Sample Problem 2
• What is the perimeter of
the parking lot in yards?
(1) 600
(2) 540
(3) 470
(4) 430
(5) 300
Sample Problem 3
• Find the area of the
parking lot in square
yards.
(1) 16,800
(2) 15,500
(3) 14,400
(4) 11,900
(5) 10,800
Sample Problem 3
• Find the area of the
parking lot in square
yards.
(1) 16,800
(2) 15,500
(3) 14,400
(4) 11,900
(5) 10,800
Sample Problem 4
• The Park family is planning to carpet their family room,
which measures 18 feet by 24 feet. They will not need to
carpet the fireplace hearth, a 3-ft-by-6-ft area centered on
one of the 18-foot walls. How many square yards of carpet
will they need?
Sample Problem 4
• The Park family is planning to carpet their family room,
which measures 18 feet by 24 feet. They will not need to
carpet the fireplace hearth, a 3-ft-by-6-ft area centered on
one of the 18-foot walls. How many square yards of carpet
will they need?
Answer:
46 square yards
Sample Problem 4
• Total area of the room (18 x 24 = 432 sq ft)
• Floor area covered by the hearth (3 x 6 = 18 sq ft)
• 432 sq ft - 18 sq ft = 414 sq ft.
• Convert 414 square
feet to square yards.
(Remember, 9 sq ft =
1 sq yd.)
Sample Problem 5
• A small solar-powered aircraft flew
5.4 hours. If the aircraft averaged 30
miles per hour, how many miles did
it travel?
Sample Problem 5
• A small solar-powered aircraft flew
5.4 hours. If the aircraft averaged 30
miles per hour, how many miles did
it travel?
• Answer: 162 miles
Sample Problem 5: Illustration
Sample Problem 6
• To find the length of a lake, we pointed
two flags at both ends of the lake, say A
and B. Then a person walks to another
point C such that the angle ABC is 90.
Then we measure the distance from A to
C to be 150m, and the distance from B to
C to be 90m. Find the length of the lake.
Sample Problem 6
• To find the length of a lake, we pointed two
flags at both ends of the lake, say A and B.
Then a person walks to another point C
such that the angle ABC is 90. Then we
measure the distance from A to C to be
150m, and the distance from B to C to be
90m. Find the length of the lake.
• Answer:
150 m
Sample Problem 6: Illustration
Sample Problem 7
• A television screen measures
approximately 15 in. high and 19 in. wide.
A television is advertised by giving the
approximate length of the diagonal of its
screen. How should this television be
advertised?
Sample Problem 7
• A television screen measures
approximately 15 in. high and 19 in. wide.
A television is advertised by giving the
approximate length of the diagonal of its
screen. How should this television be
advertised?
Answer:
21 inches TV Screen
Topics:
• Session 1: Basic Formulas and Data
Presentation
• Session 2: Table, Charts, Graphs and
Coordinate Grids
• Session 3: Basic Statistics
Session 2: Objectives
1. Interpret and compare data from graphs
(including circle, bar, and line graphs), charts,
and tables;
2. Identify x- and y-axes, point of origin,
quadrants, coordinates, and ordered pairs; and
3. Read, interpret, and plot points in any of the
quadrants.
Table, Charts, Graphs and Coordinate
Grids
• The behavior of a variable and the relationship
between two variables in a real-world context
may be explored by considering data presented
in tables and graphs.
• The ability to interpret and synthesize data from
charts, graphs, and tables is a widely applicable
skill in college and in many careers
Table, Charts, Graphs and Coordinate
Grids
• Charts combine pictures and information.
Geometric figures and arrows can help you
understand how, when, and where events took
place.
• The coordinate grids has similar elements to
the coordinate planes. It consists of a horizontal
axis and a vertical axis, number lines that
intersect at right angles.
Table, Charts, Graphs and Coordinate
Grids
• The horizontal axis in the coordinate plane is called
the x-axis. The vertical axis is called the y-axis. The
point at which the two axes intersect is called the
origin. The origin is at 0 on the x-axis and 0 on the yaxis.
• The intersecting x- and y-axes divide the coordinate
plane into four sections. These four sections are
called quadrants. Quadrants are named using the
Roman numerals I, II, III, and IV beginning with the
top right quadrant and moving counter clockwise.
Table, Charts, Graphs and Coordinate
Grids
• Locations on the coordinate plane are described
as ordered pairs. An ordered pair tells you the
location of a point by relating the point’s
location along the x-axis (the first value of the
ordered pair) and along the y-axis (the second
value of the ordered pair).
Table, Charts, Graphs and Coordinate
Grids
• In an ordered pair, such as (x, y), the first value
is called the x-coordinate and the second value is
the y-coordinate. Note that the x-coordinate is
listed before the y-coordinate. Since the origin
has an x-coordinate of 0 and a y-coordinate of 0,
its ordered pair is written (0, 0).
Table, Charts, Graphs and Coordinate
Grids
Sample
Problem 1
• One evening, Maria walks,
jogs, and runs for a total of
60 minutes. The graph
above shows Maria’s speed
during the 60 minutes.
Which segment of the
graph represents the times
when Maria’s speed is the
greatest?
A) The segment from (17, 6) to (19, 8)
B) The segment from (19, 8) to (34, 8)
C) The segment from (34, 8) to (35, 6)
D) The segment from (35, 6) to (54, 6)
Sample
Problem 1
• One evening, Maria walks,
jogs, and runs for a total
of 60 minutes. The graph
above shows Maria’s
speed during the 60
minutes. Which segment
of the graph represents
the times when Maria’s
speed is the greatest?
A) The segment from (17, 6) to (19, 8)
B) The segment from (19, 8) to (34, 8)
C) The segment from (34, 8) to (35, 6)
D) The segment from (35, 6) to (54, 6)
Sample Problem 2
• A store is deciding whether to install a new security system to prevent
shoplifting. Based on store records, the security manager of the store
estimates that 10,000 customers enter the store each week, 24 of whom
will attempt to shoplift. Based on data provided from other users of the
security system, the manager estimates the results of the new security
system in detecting shoplifters would be as shown in the table below
Sample Problem 2
• According to the manager’s estimates, if the alarm sounds for a
customer, what is the probability that the customer did not attempt to
shoplift?
A) 0.0003
B) 0.0035
C) 0.0056
D) 0.625
Sample Problem 2
• According to the manager’s estimates, if the alarm sounds for a
customer, what is the probability that the customer did not attempt to
shoplift?
A) 0.0003
B) 0.0035
C) 0.0056
D) 0.625
Sample Problem 3
• In 1998, Mark McGwire hit
more home runs than any
individual had ever hit in a
single season. The chart shows
the locations of his 70 home
runs. To which location did he
hit nearly 20% of his home
runs?
Sample Problem 3
• In 1998, Mark McGwire hit
more home runs than any
individual had ever hit in a
single season. The chart shows
the locations of his 70 home
runs. To which location did he
hit nearly 20% of his home
runs?
Answer:
Center Field
Sample Problem 4
Political opinion polls often use
graphics to represent election results.
This double-bar graph shows how
many votes were received by two
candidates in two districts
Is the following statement true? In the
18th District, Ms. Black received
about four times as many votes as Dr.
Green.
Sample Problem 4
Is the following statement true? In the
18th District, Ms. Black received about
four times as many votes as Dr. Green.
Answer:
The statement is false. Read the lefthand scale carefully to see that Ms.
Black received twice as many votes.
Note: A graph can appear misleading if the
scale doesn’t start at 0.
Sample Problem 5
The graph below shows the
performance of two stocks,
ARL and CTR, over a 5-week
period
Sample Problem 5
1. On March 26, what was the
approximate cost of one
share of CTR stock?
2. Which stock has shown the
greatest increase in price
over the 5-week period?
Sample Problem 5
1. On March 26, what was the
approximate cost of one
share of CTR stock?
Answer: About $82
2. Which stock has shown the
greatest increase in price
over the 5-week period?
Answer: CTR stock
You are looking for the
greatest change in price,
not the highest price
Sample Problem 5
3. Guido bought 5 shares of
ARL stock on March 5.
Approximately how much
did he pay for the shares?
4. Based on the current trends,
which stock will be worth
more per share by the end
of April?
Sample Problem 5
3. Guido bought 5 shares of
ARL stock on March 5.
Approximately how much did
he pay for the shares?
Answer: $450 Multiply $90
by 5.
4. Based on the current trends,
which stock will be worth
more per share by the end of
April? Answer: CTR stock
The line representing CTR
is climbing faster than the
line for ARL. The CTR line
is likely to cross the ARL
line in the very near future.
Sample Problem 5
5. By about how much money
did the price of a share of
CTR stock increase from
March 19 to March 26?
Sample Problem 5
5. By about how much money
did the price of a share of
CTR stock increase from
March 19 to March 26?
Answer: About $20
Topics:
• Session 1: Basic Formulas and Data
Presentation
• Session 2: Table, Charts, Graphs and
Coordinate Grids
• Session 3: Basic Statistics
Session 3: Objectives
1. Compute the mean, median, mode, and range
of distributions.
2. Facilitate comparison and facilitate statistical
analysis.
Basic Statistics
• One way we analyze data is to look at measures
of central tendency—mean, median, and mode.
• They are the tools to look at the information for
the purpose of answering the question, “What is
normal?”
Basic Statistics
• Understanding the measures of central tendency
can help us make important life decisions. For
example, averages can help us set goals or plan
budgets.
Basic Statistics
• Data is bits of information. It is often in
numerical terms.
• Mean, median, and mode are different ways to
describe the typical values of a set of data.
Basic Statistics
• The “mean, or average”, tells us what number
may be used to represent a group of numbers. It
is found by adding all the data, then dividing the
total by the number of items.
• The “median” is the number in the middle of a
range of data that has been ordered from least to
greatest.
Basic Statistics
• The “mode” is the piece of data that appears
most often, or the number that is repeated the
most times in the collection of data. It does not
have to be calculated, just identified by
observation.
• The "range" of a list a numbers is just the
difference between the largest and smallest
values.
Find the mean, median, mode, and range for the following
list of values:
• 13, 18, 13, 14, 13, 16, 14, 21, 13
• The mean is the usual average, so I'll add and then divide:
= (13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9
= 15
Note that the mean, in this case, isn't a value from the original
list. This is a common result. You should not assume that your
mean will be one of your original numbers.
The median is the middle value, so first I'll have to
rewrite the list in numerical order:
13, 13, 13, 13, 14, 14, 16, 18, 21
There are nine numbers in the list, so the middle one will be
the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:
13, 13, 13, 13, 14, 14, 16, 18, 21
So the median is 14.
The mode is the number that is repeated more often than any
other, so 13 is the mode.
The largest value in the list is 21, and the smallest is 13, so the range is
21 – 13 = 8
mean: 15 ; median: 14; mode: 13; range: 8
Note: The formula for the place to find the median is "([the number
of data points] + 1) ÷ 2", but you don't have to use this formula. You
can just count in from both ends of the list until you meet in the
middle, if you prefer, especially if your list is short. Either way will
work.
Find the mean, median, mode, and range for the
following list of values:
8, 9, 10, 10, 10, 11, 11, 11, 12, 13
The mean is the usual average, so I'll add up and then divide:
= (8 + 9 + 10 + 10 + 10 + 11 + 11 + 11 + 12 + 13) ÷ 10
= 105 ÷ 10
= 10.5
The median is the middle value. In a list of ten values, that will
be the (10 + 1) ÷ 2 = 5.5-th value; the formula is reminding
me, with that "point-five", that I'll need to average the fifth
and sixth numbers to find the median. The fifth and sixth
numbers are the last 10 and the first 11, so:
(10 + 11) ÷ 2 = 21 ÷ 2 = 10.5
The mode is the number repeated most often. This list has
two values that are repeated three times; namely, 10 and 11,
each repeated three times.
The largest value is 13 and the smallest is 8, so the range is
=13 – 8 = 5.
mean: 10.5; median: 10.5; modes: 10 and 11; range: 5
As you can see, it is possible for two of the averages (the mean
and the median, in this case) to have the same value. But this is
not usual, and you should not expect it.
Exer. Problem 1
The table below shows the
data Steve collected while
watching birds for one week.
How many raptors did Steve
see on Monday?
(1) 6 raptors
(2) 7 raptors
(3) 8 raptors
(4)10 raptors
Exer. Problem 1
The table below shows the
data Steve collected while
watching birds for one week.
How many raptors did Steve
see on Monday?
(1) 6 raptors
(2) 7 raptors
(3) 8 raptors
(4)10 raptors
Exer. Problem 2
The Jerry wants to find the mode and the
median of his nine art project scores: 91,
83, 69,91, 87, 83, 80, 83, 89. He makes a
stem-and-leaf plot, ordering the tensplace digits (the stem) from largest to
smallest. The ones-place digits (the
leaves) are listed from smallest to largest.
Jerry records each score, including repeat
scores.
Exer. Problem 1
Answer:
Mode:
83
Median: 83
Exer. Problem 3
Juanita’s electric bills for the past four months were $65.23,
$49.37, $70.01, and $55.27. What was the median amount of her
electric service for those months?
(1) $59.97
(2) $60.25
(3) $70.01
(4) $120.50
(5) $239.88
Exer. Problem 3
Juanita’s electric bills for the past four months were $65.23,
$49.37, $70.01, and $55.27. What was the median amount of her
electric service for those months?
(1) $59.97
(2) $60.25
(3) $70.01
(4) $120.50
(5) $239.88
Exer. Problem 4
Janelle and Pat Rosarian have five children.The twins are 14 years
old. The other children are 4, 7, and 11 years old.
What is the average age of the Rosarian children?
(1) 8
(2) 9
(3) 10
(4) 11
(5) 14
Exer. Problem 4
Janelle and Pat Rosarian have five children.The twins are 14 years
old. The other children are 4, 7, and 11 years old.
What is the average age of the Rosarian children?
(1) 8
(2) 9
(3) 10
(4) 11
(5) 14
Exer. Problem 5
Janelle and Pat are aged 38 and 43, respectively. Which
expression might you use to determine the mean age for the
entire family?
(1) 7(14+14+4+7+11+38+43)
(2)
50
5
(3)
50
7
(4)
50
5
(5)
131
7
+
38+43
2
Exer. Problem 5
Janelle and Pat are aged 38 and 43, respectively. Which
expression might you use to determine the mean age for the
entire family?
(1) 7(14+14+4+7+11+38+43)
(2)
50
5
(3)
50
7
(4)
50
5
(5)
𝟏𝟑𝟏
𝟕
+
38+43
2
Exer. Problem 6
Pat’s age is approximately how many times the age of the middle
Rosarian child?
(1) 10
(2) 4
(3) 3
(4) 2
(5) Not enough information is given.
Exer. Problem 6
Pat’s age is approximately how many times the age of the middle
Rosarian child?
(1) 10
(2) 4
(3) 3
(4) 2
(5) Not enough information is given.
Exer. Problem 7
A student has gotten the following grades on his tests: 87, 95, 76,
and 88. He wants an 85 or better overall. What is the minimum
grade he must get on the last test in order to achieve that
average?
The minimum grade is what we need to find. To find the average
of all his grades (the known ones, plus the unknown one), we
have to add up all the grades, and then divide by the number of
grades. Since we don't have a score for the last test yet, we'll use a
variable to stand for this unknown value: "x". Then computation
to find the desired average is:
Exer. Problem 7
A student has gotten the following grades on his tests: 87, 95, 76, and
88. He wants an 85 or better overall. What is the minimum grade he
must get on the last test in order to achieve that average?
(87 + 95 + 76 + 88 + x) ÷ 5 = 85
Multiplying through by 5 and simplifying, we get:
87 + 95 + 76 + 88 + x = 425
346 + x = 425
x = 79
Thank you for listening