Stat & Prob ch 2

The difference between the maximum and minimum member of a data set.

The difference between the lower (or upper) limits of two adjacent classes.

The midpoint of the interval between the upper limit of a class and the lower limit of the next class

The midpoint of the interval between the lower and upper limits of a class.

The number of scores that fall in a class.

The number of scores that fall in a class

The sum of frequencies for a specific class and all classes below it.

A bar diagram where each bar corresponds to one of the classes, and its height is equal to class' frequency (to some scale).

a Graph of cumulative frequency distribution

A circular diagram depicting the distribution of qualitative data.

A representative or average value that indicates where the middle of the data set is located.

A measure of the amount that the data values vary.

The nature or shape of the spread of the data over the range of values (such as bell-shapred, uniform, or skewed).

Sample values that lie very far away from the vast majority of the other sample values.

Changing characteristics of the data over time

Center, Variation, Distribution, Outliers, Time

• (maximum data value) - (Minimum data value)
• Number of classes

5 & 20

• class frequency
• sum of all frequencies

• Class frequency
• sum of all frequency x 100%

The average value of all members of a data set

The middle value of a data set that is arranged in ascending or descending order.

The value most frequently occurring in a data set.

The half-sum of the minimum and maximum value of a data set.

The mean of a data set whose members have a different significance (weight) w:

The measure of a distribution’s asymmetry. (A left-skewed distribution has a peak shifted to the right, and vice versa.)

A measure of variation taking into account each member of a data set.

A relative measure of variation.

• A measure of relative standing, showing how many standard deviations the given value is below or
• above the mean.

Any values that are more than two standard deviations below or above the mean.

Characteristic values dividing a data set (arranged in ascending/descending order) in quarters.

The difference between the third and the first quartile.

An extremely small or extremely large value in a data set.

demotes the sum of a set of data values

is the variable usually used to represent the individual data values.

represents the number of data values in a sample

represents the number of data values in a populations.

An action involving uncertainty and consisting of a number of trials for which an outcome (measurement, response etc.) is obtained.

The set of all possible outcomes of an experiment.

A collection of outcomes.

An event that includes just one outcome.

An event that includes two or more outcomes.

If the experiment was performed m times and event A occurred f times, then the probability of event A is

• If the number of simple events (sample space size) is n and the number of ways the event A can occur is s, then
• the probability of event A is

A probability that is based on intuitive feeling rather than on logical reasoning.

The larger is the number of trials, the closer is the probability by Rule 1 to the actual probability.

The probability of an event may be a number in the interval from 0 to 1 inclusive.

The probability of an impossible event is 0.

The probability of an event that is certain to occur is 1.

Two events such that one or the other must occur, but not both at the same time.

The probability that either event A occurs, or event B occurs, or both occur at the same time is

P(A or B) = P(A) + P(B) – P(A and B)

• where P(A and B) is the probability that both A and
• B occur at the same time.

Two events that cannot occur at the same time.

P(A or B) = P(A) + P(B)

• If two events A and are complementary, then
• 

• The probability of event B occurring under condition
• that event A has occurred.

Two event (A and B) such that the probability of B does not depend on whether A occurred or not.

• The probability of events A and B occurring consequently is
• P(A and B) = P(A)×P(B½A)

P(A and B) = P(A)×P(B)

P (at least 1) = 1 – P(0)

• If a procedure consists of two events, such that one can occur in m ways and the other in n ways,
• the whole procedure can occur in m·n ways.

The same principal is applicable to a procedure consisting of more than two events.

The product = n! is called n factorial.

This definition applies to n> 1. 0! = 1.

The number of ways r items can be selected from a set of n items (r < n) and arranged in all possible orders is

• 
• Another form of this formula:

n different items can be arranged in n! ways.

• The number of ways r items can be selected
• from a set of n items (r < n) is