MATH EXAM 1 Review

Permutation Theorem

Number of permutations of r objects out of a total set of n objects when repetition is not allowed. You cannot use the object more than once Formula: nPr= n!/(n-r)! R-Studio Command: factorial(n)/factorial(n-r) if Repetition is allowed: n^2

Permutation, n(object taken n at a time with) r(objects alike), s(of another kind alike) t(of another kind alike is:

P= n!/r!s!t! R-Studio Command: factorial(n)/(factorial(r)*factorial(s)*factorial(t))

Event

A set of outcomes; a subset of the sample space

Sample Data

A small section of a population taken for the purpose of an investigation

Independent

2 events are independent if knowing that one of the events occur does not affect the probability that the other occurs If E and F are independent events, then P(EunionF) = P(E)P(F)

Outliers

An observation that is "distant" from the rest of the data. To find it: 1.) fivenum(data) 2.) Find IQR : Q3-Q1 3.) Q1-1.5(IQR) 4.) Q3+1.5(IQR)

Combination n( total number) r( number you are choosing)

An unordered subset of outcomes nCr = n!/ r!(n-r)! R-Studio Command choose(n,r)

Variance

Average squared distance of a data set from the mean of the data set Command: var(data)

Quantitative - Continuous Data

Data that can take on any values within some interval. Its a variable thats obtained by measuring. Examples: -The weight of an 11yr old male. -Grade point average of students at a particular high school -Weight, height, time, distance

Categorical Variable

Describe qualities or attributes of an individual. Examples: -Favorite color -preferred political party -blood type

Population Data

Everything or everyone of interest to our study. It is the set that consists of all possible values

A sample is the set of all possible data values for a given subject under consideration. True or False

False

Of the range, the interquartile range, and the variance, the interquartile range is most influence by an outlying value in the data set. True or False

False

Range

Found by subtracting the minimum data value from the maximum data value

Interquartile Range (IQR)

Found by using the command "fivenum"(data) on R-Studio, then subtracting the Q3-Q1

Quantitative - Discrete Data

Is a countable set of values. A variable that is obtained by counting. Example: -The number of sodas consumed at a restaurant in a day - Amount of money in a piggy bank -Age of people when they first get their license

Sample Space

Set of all possible outcomes of a random experiment or of an arrangement or choice

Mean

The numeric average of a set of quantitative data. Command on R-Studio mean(data)

Permutation

The ordered arrangement of objects in a set Formula: nPn=n*(n-1)*(n-2)*(n-3)...=n! R-Studio: factorial(n)

Probability E- Number of outcomes in the event S- Number of outcomes in the sample space:

The proportion of times an event would occur in a very long (infinite) series of repetitions P(E)= n(E)/n(S)

Standard Deviation

The square root of the variance Command on R-Studio for Sample SD sqrt(var(data)) or sd(data)

Fundamental Counting Principle

The total number of a ways a compound event may occur: n1*n2*n3*...*n

Mode

The value that occurs most often in a set of data. Command on R-studio mode(data)

The standard deviation is the square root of the variance. True or False

True

Median

Which is Q2 is the 50th percentile of the ordered data. The value at the middle of the data set Command on R-Studio median(data)

The union of two events A and B is the event that: a.) Either A or B, but not both occur b.) Both A and B occur c.) A and B occur at the same time d.) The intersection of A and B does not occur e.) Either A or B or both occur f.) None of the above

b.) Both A and B occur

Which of the following is a measure of variation? a.) mean b.) standard deviation c.) median d.) mode

b.) standard deviation

Boxplot R-Studio Command

boxplot(data,xlab="data(in.)",horizontal=T)

Given a data set of all positive values, if the largest value of a data set is doubled, which of the following is not true? a.) The mean increases b.) The range increases c.) The interquartile range increases d.) The standard deviation increases

c.) The interquartile range increases.

If a distribution has a zero variance, which of the following is true? a.) The number of positive values and the number of negative values are equal. b.) All the values are positive c.) All the values are negative d.) All the values are equal to each other

d.) All the values are equal to each other

Given the first type of plot indicated in each pair, which of the second plots could not always be generated from it? a.) dot plot, histogram b.) dot plot, stem and leaf c.) steam and leaf, dot plot d.) box plot, steam and leaf

d.) box plot, steam and leaf