Data Analysis, Statistics, and Probability Review

The SAT doesn’t includecomputation of standard deviation

Data Interpretation

• interpret information in graphs, tables, or charts

• then compare quantities, recognize trends and changes in the data

• perform calculations based on the information you have found

Graphs

Circle Graphs

Line Graphs

Bar Graphs

Pictographs

Scatterplot

Data Interpretation Questions

When working with data interpretation questions:

• Look at the graph, table, or chart to make sure you understand it.

• Make sure you know what type of information is being displayed.

• Read the labels. • Make sure you know the units. • Make sure you understand what is

happening to the data as you move through the table, graph, or chart.

• Read the question carefully.

Example:In what month did the profits of the

two companies show the greatest difference?

Since the distance between the two graph points is greatest at April, that is the answer.

Example: If the rate of increase or decrease for each

company continues for the next six months at the same rate shown between April and May, which company would have higher profits at the end of that time?

Answer is Company Y. Extend the lines out and

Company Y crosses to go above Company X.

Example:

As an experiment, Josh bought 20 different batteries of various brands and prices. He tested each battery to see how long it would keep a toy car working before losing power. For each battery, he plotted the duration against the price. Of the five labeled points, which one corresponds to the battery that cost the least per length of duration?

Answer: Cost per hour of duration is price/time which is the slope of each line drawn from the Origin to a Point.

has the smallest slope so battery C has the least cost per hour of duration.

OC

StatisticsArithmetic Mean• average

•

Median• middle value of a list when the numbers are

in order Mode• value or values that appear the greatest

number of times

sum of list of values

number of values in list

Weighted Average• average of two or more groups that do not

all have the same number of members

Example:

What is the average of Ms. Smith’s Geometry Exams if one class of 27 students averaged 84%, another class of 10 students averaged 70% and her third class of 15 students had an average of 62%?

Answer is 75% rounded to the nearest tenth.

27 84 10 70 15 6274.96 75%

27 10 15

Average of Algebraic Expressions• also called arithmetic mean

Example: Find the arithmetic mean of 3x+4 and 5x -

10.Answer: 3 4 5 10 8 6

4 32 2

x x xx

Using Averages to Find Missing Numbers

• average =

• therefore, average number of values = sum of values

Example: Sean has test scores of 88, 83, 72 and 90. What does he need to make on his fifth test to have an 85 average?

Answer: 85 x 5 = 425 88 + 83 +72 +90 = 333 425 – 333 = 92

sum of list of values

number of values in list

ProbabilityProbability of Event• number between 0 and 1, inclusive• if an event is certain, it has probability 1• if an event is impossible, it has probability 0Independent Events• the outcome of either event has no effect on

the other• to find the probability of two or more

independent events occurring together, multiply the probabilities of the individual events

Dependent Events

• the outcome of one event affects the probability of another event

• use logical reasoning to help figure out probabilities involving dependent events

Example: Given the large circle has radius 8 and the small circle has radius 2. If a point is chosen at random from the large circle, what is the probability that the point chosen will be in the small circle?

2(8) 64

Geometric Probability• Probability involving geometric figures

Answer: Area of large circle =Area of small circle =So the probability of the point being in the small circle is .

2(2) 4

4 1

64 16

Example:A game at the state fair has a circular target

with a radius of 10.7 cm on a square board measuring 30 cm on a side. Players win prizes if they throw a dart and hit the circular area only. What is the probability of winning with one throw of a dart?

measure of geometric model representingP(E) = desired outcomes in the event

measure of geometric model representing all outcomes in the same space

Solution:Area of circle A = Area of entire square board A =

P (E) = or 40% chance of hitting in the circle.

2(10.7) 359.7 230 900

359.7.40

900