Stat & Prob ch 2
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Stat & Prob ch 2
Statistics probability chapter lecture
Statistics and Probability chapter 2 lecture
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
The number of classes should be between
5 & 20
sum of all frequencies
Percentage 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.
Population standard deviation
Sample standard deviation
Coefficient of variation (CV)
A relative measure of variation.
z- score (standardized value)
A measure of relative standing, showing how many standard deviations the given value is below or
above the mean.
Unusually small or unusually large values
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.
Interquartile range (IQR)
The difference between the third and the first quartile.
An extremely small or extremely large value in a data set.
of a set of data values
usually used to represent the individual data values.
number of data values
number of data values
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.
Probability Rule 1 (Relative Frequency Approximation)
If the experiment was performed m times and event A occurred f times, then the probability of event A is
Probability Rule 2 (Classical Approach)
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.
Law of Large Numbers
The larger is the number of trials, the closer is the probability by Rule 1 to the actual probability.
Range of 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.
Formal Addition Rule
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.
Mutually exclusive (disjoint) events
Two events that cannot occur at the same time.
Addition Rule for mutually exclusive events
P(A or B) = P(A) + P(B)
Rule of Complementary Events
If two events A and are complementary, then
Conditional probability (probability of B given A)
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.
Formal Multiplication Rule
The probability of events A and B occurring
P(A and B) = P(A)×P(B½A)
Multiplication Rule for independent events
P(A and B) = P(A)×P(B)
Rule of At Least One
P (at least 1) = 1 – P(0)
Fundamental Counting Rule
If a procedure consists of two events, such that one can occur in m ways and the other in
the whole procedure can occur in
The same principal is applicable to a procedure consisting of more than two events.
= n! is called n factorial.
This definition applies to n> 1. 0! = 1.
Permutation Rule (when all items are different)
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