chapglos_summaries

7/29/2019 ChapGlos_Summaries

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Chapter 1

Descriptive statistics - The techniques used to describe the important characteristics of a set of data.

This includes organizing the data values into a frequency distribution, computing measures of location,

and computing measures of dispersion and skewness.

Inferential statistics, also called statistical inference - This facet of statistics deals with estimating a

population parameter based on a sample statistic. For example, if a sample of 10 TI-36X solar calculators

revealed 2 to be defective, we might infer that 20 percent of the production is defective.

Interval measurement - If one observation is greater than another by a certain amount, and the

zero point is arbitrary, the measurement is on an interval scale. For example, the difference between

temperatures of 70 degrees and 80 degrees is 10 degrees. Likewise, a temperature of 90 degrees is 10

degrees more than a temperature of 80 degrees, and so on.

Nominal measurement - The lowest level of measurement. If data are classified into categories

and the order of those categories is not important, it is the nominal level of measurement. Examples aregender (male, female) and political affiliation (Republican, Democrat, Independent, all others). If it

makes no difference whether male or female is listed first, the data are nominal level.

Ordinal measurement - Data that can be ranked are referred to as ordinal measures. For

example, consumer response to the sound of a new speaker might be excellent, very good, fair, or poor.

Population - The collection, or set, of all individuals, objects, or measurements whose properties are

being studied.

Ratio measurement - If the distance between numbers is a constant size, there is a true zero point,

and the ratio of two values is meaningful, then the data are ratio scale. For example, the distancebetween $200 and $300 is $100, and in the case of money there is a true zero point. If you have zero

dollars, there is an absence of money (you have none). Also the ratio between $200 and $300 is

meaningful.

Sample - A portion, or subset, of the population being studied.

Statistics - The science of collecting, organizing, analyzing, and interpreting numerical data for the

purpose of making more effective decisions.

Chapter 2

Charts - Special graphical formats used to portray a frequency distribution, including histograms,

frequency polygons, and cumulative frequency polygons. Other graphical devices used to portray data

are bar charts and pie charts.


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Class - The interval in which the data are tallied. For example, $4 up to $7 is a class; $7 up to

$11 is another class.

Class frequency - The number of observations in each class. If there are 16 observations in the $4

up to $6 class, 16 is the class frequency.

Exhaustive - Each observation must fall into one of the categories.

Frequency distribution - A grouping of data into classes showing the number of observations in

each of the mutually exclusive classes.

Histogram - A graphical display of a frequency or relative frequency distribution. The horizontal axis

shows the classes. The vertical height of adjacent bars shows the frequency or relative frequency of

each class.

Midpoint- The value that divides the class into two equal parts. For the classes $10 up to $20 and

$20 up to $30, the midpoints are $15 and $25, respectively. Mutually exclusive A property of a set of

categories such that an individual, object, or measurement is included in only one category.

Relative frequency distribution - A frequency distribution that shows the fraction or proportion

of the total observations in each class.

Chapter 3

Arithmetic mean- The sum of the values divided by the number of values. The symbol for the

mean of a sample is and the symbol for a population mean is .

Geometric mean - The nth root of the product of all the values. It is especially useful for averaging

rates of change and index numbers. It minimizes the importance of extreme values. A second use of the

geometric mean is to find the mean annual percent change over a period of time. For example, if gross

sales were $245 million in 1990 and $692 million in 2010, the average annual rate of return is 5.33

percent.

Mean deviation - The mean of the deviations from the mean, disregarding signs. It is identified as

MD.

Measure of dispersion - A value that shows the spreadof a data set. The range, variance, and

standard deviationare measures of dispersion.

Measure of location - A single value that is typical of the data. It pinpoints the center of a distribution.

The arithmetic mean, weighted mean, median, mode, and geometric mean are measures of location.

Median - The value of the middle observation after all the observations have been arranged from

low to high. For example, if observations 6, 9, 4 are rearranged to read 4, 6, 9, the median is 6, the

middle value.


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Mode - The value that appears most frequently in a set of data. For grouped data, it is the

midpoint of the class containing the largest number of values.

Range - It is a measure of dispersion. The range is found by subtracting the minimum value from

the maximum value.

Standard deviation - The square root of the variance.

Variance - A measure of dispersion based on the average squared differences from the arithmetic

mean.

Weighted mean - Each value is weighted according to its relative importance. For example, if 5

shirts cost $10 each and 20 shirts cost $8 each, the weighted mean price is $8.40(5x10)+(20x8)/25

Chapter 4

Box plot - A graphic display that shows the general shape of a variables distribution. It is based on

five descriptive statistics: the maximum and minimum values, the first and third quartiles, and the

median.

Coefficient of skewness - A measure of the lack of symmetry in a distribution. For a symmetric

distribution there is no skewness, so the coefficient of skewness is zero. Otherwise, it is either positive

or negative, with the limits of (+-)3.0.

Contingency table - A table used to classify observations according to two characteristics.

Deciles- Values of an ordered (minimum to maximum) data set that divide the data into tenequal parts.

Dot plot - A dot plot summarizes the distribution of one variable by stacking dots at points on a

number line that shows the values of the variable. A dot plot shows all values.

Interquartile range - The absolute numerical difference between the first and third quartiles. Fifty

percent of a distributions values occur in this range.

Outlier - A data point that is usually far from the others. An accepted rule is to classify an

observation as an outlier if it is 1.5 times the interquartile range above the third quartile or below the

first quartile.

Percentiles- Values of an ordered (minimum to maximum) data set that divide the data into one

hundred intervals.

Quartiles- Values of an ordered (minimum to maximum) data set that divide the data into four

intervals.


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Scatter diagram - Graphical technique used to show the relationship between two variables

measured with interval or ratio scales.

Stem-and-leaf display- A method to display a variables distribution using every value. Values

are classified by the datas leading digit. For example, if a data set contains values between 13 and 84,

eight classes based on the 10s digit would be used for the stems. The 1s digits would be the leaves.

Chapter 5

Bayes theorem - Developed by Reverend Bayes in the 1700s, it is designed to find the

probability of one event, A, occurring, given that another event, B, has already occurred.

Classical probability- Probability based on the assumption that each of the outcomes is

equally likely. According to this concept of probability, if there are n possible outcomes, the probability

of a particular outcome is 1/n. Thus, on the toss of a coin, the probability of a head is 1/n

1/2.

Combination formula- A formula to count the number of possible outcomes when the order of

the outcomes is not important. If the order a, b, c is considered the same as b, a, c, or c, b, a, and so on,

the number of arrangements is found by:

Conditional probability - The likelihood that an event will occur given that another event

has already occurred.

Empirical probability - A concept of probability based on past experience. For example,

Metropolitan Life Insurance Company reported that, during the year, 100.2 of every 100,000 persons in

Wyoming died of accidental causes (motor vehicle accidents, falls, drowning, firearms, etc.). On the

basis of this experience, Metropolitan can estimate the probability of accidental death for a particular

person in Wyoming: 100.2/100,000 .001002.

Event - A collection of one or more outcomes of an experiment. For example, an event is the

collection of even numbers in the roll of a fair die.

Experiment - An activity that is either observed or measured. An experiment may be counting

the number of correct responses to a question, for example.

General rule of addition - Used to find the probabilities of complex events made up of Aor B when the events are not mutually exclusive.

General rule of multiplication- Used to find the probabilities of events A and B both happening

when the events are not independent. Example: It is known that there are 3 defective radios in a box

containing 10 radios. What is the probability of selecting 2 defective radios on the first two selections

from the box? Where P(B|A) is the conditional probability and means the probability of B occurring

given that A has already occurred.


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Independent- The probability of one event has no effect on the probability of another event.

Multiplication formula - One of the formulas used to count the number of possible

outcomes of an experiment. It states that if there are m ways of doing one thing and n ways of doing

another, there are m x n ways of doing both. Example: A mens clothier offers two sport coats and three

contrasting pants for $400. How many different outfits can there be? Answer: m x n = 2 x 3 = 6

Mutually exclusive - The occurrence of one event means that none of the other events can

occur at the same time.

Outcome A particular observation or measurement of an experiment.

Permutation formula - A formula to count the number of possible outcomes when the order of

the outcomes is important. If a, b, c is one arrangement, b, a, c another, c, a, b another, and so on, the

total number of arrangements is determined by

Probability- A value between 0 and 1, inclusive, that reports the likelihood that a specific event will

occur. Special rule of addition For this rule to apply, the events must be mutually exclusive. For two

events, the probability of A or B occurring is found by: Example: The probability of a one-spot or a two-

spot occurring on the toss of one die.

Special rule of multiplication - If two events are not relatedthat is, they are independent

this rule is applied to determine the probability of their joint occurrence. Example: The probability of

two heads on two tosses of a coin is:

Subjective probability- The chance of an event happening based on whatever information is

available hunches, personal opinion, opinions of others, rumors, and so on.

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