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# Mathematics 217

### Chapters 9 - 10

Term | Definition |
---|---|

Experiment | An activity whose results can be observed and recorded. |

Outcome | Each of the possible results of an experiment. |

Sample space | A set of all possible outcomes for an experiment. |

Event | Any subset of a sample space. |

Experimental (empirical) probability | The empirical probability of an event occurring is the “fraction” of the number of times the event occurred divided by the number of times the experiment was performed. |

Law of large numbers (Bernoulli's theorem) | If an experiment is repeated a large number of times, the experimental (empirical) probability of a particular outcome approaches a fixed number as the number or repetitions increases. |

Experimental (empirical) probability | Experimental (empirical) probability is determined by observing outcomes of experiments. |

Theoretical probability | The outcome under ideal conditions. |

Equally likely | When one outcome is as likely as another. |

Uniform sample space | Each possible outcome of the sample space is equally likely. |

Impossible event | An event with no outcomes; has probability 0. |

Certain event | An event with probability 1. |

Probability theorem | The probability of an event is equal to the sum of the probabilities of the disjoint outcomes making up the event. |

Mutually exclusive event | Events A and B are mutually exclusive if they have no elements in common. |

Mutually exclusive event | The probability of the union of mutually exclusive events is the sum of the probabilities of those events. |

Complementary event | Two mutually exclusive events whose union is the sample space are complementary events. |

Multiplication rule for probabilities for tree diagram | For all multistage experiments, the probability of the outcome along any path of a tree diagram is equal to the product of all the probabilities along the path. |

Independent event | When the outcome of one event has no influence on the outcome of a second event. |

Computing odds | The odds of an event occurring or not occurring are expressed as a ratio of the probabilities. |

Conditional probability | If A and B are events in sample space S and P (A) is not equal to 0, then the conditional probability that an event B occurs given that event A has occurred. |

Expected value | Expected value can be used to predict the average result of an experiment when it is repeated many times. Expected value cannot be used to determine the outcome of any single experiment. |

Permutations of unlike objects | If an event M can occur in m ways and event N can occur in n ways, then the number of ways event M followed by event N can occur is m·n. |

Permutation | An arrangement of things in a definite order with no repetitions. |

Permutations involving like objects | If there are n objects, of which r1 are alike, r2 are alike, and so on through rk, then the number of different arrangements of all n objects, where alike objects are indistinguishable. |

Combination | An arrangement of things in which the order makes no difference. |

Data analysis | Usually refers to a more informal approach to statistics. It is relatively new term in mathematics. |

Statistics | Once referred to numerical information about state or political territories; it comes from the Latin statisticus, meaning "of the state. " Today, much of statistics involves making sense of data. |

Data | Data are observations (such as measurements, genders, survey responses) that have been collected. |

Categorical data | Categorical data are data that represent characteristics of objects or individuals in groups(or categories), such as black or white, inside or outside, male or female. |

Numerical data | Numerical data are data collected on numerical variables. |

Pictograph | A pictograph is used to represent tallies of categories. |

Dot plots | A dot plot, or line plot, provides a quick and simple way of organizing numerical data. They are typically used when there is only one group of data with fewer than 50 values. |

Outlier | An outlier is any value that is more than 1.5 times the interquartile range above the upper quartile or below the lower quartile. An outlier is a value that is widely separated from the rest of the group of data. |

Cluster | An isolated group of points. |

Gap | A large space between data points. |

Mode | Data value(s) that occur most often. |

Stem and leaf plots | The stem and leaf plot is similar to the dot plot, but the number line is usually vertical, and digits are used rather than x’s. |

Frequency table | A grouped frequency table shows how many times data occurs in a range. |

Histogram | A histogram is made up of adjoining rectangles, or bars. |

Bar graph | A bar graph typically has spaces between the bars and is used to depict categorical data. |

Double bar graph | A double bar graph can be used to make comparisons in data. |

Circle graph (pie chart) | A circle graph, or pie chart, is used to represent categorical data. It consists of a circular region partitioned into disjoint sections, with each section representing a part or percentage of the whole. |

Line graph | A line graph typically shows trends in a variable over time. Time is usually marked on the horizontal axis, with the variable being considered marked on the vertical axis. Consecutive data points are connected by line segments. |

Scatterplot | Sometimes a relationship between variables cannot be easily depicted by even a broken line, so a scatterplot may be used. |

Trend line | A trend line is a line that closely fits the data and can be used to describe it. A trend line can be used to make predictions. |

Broken line graph | Broken line graphs may be used together to demonstrate different sets of data where comparisons may be made. |

Box plot | Box plot graph is used to show median, quartile, and extremes of data set. A box plot (or box - and - whisker plot) is a way to display data visually and draw informal conclusions. |

Mean | The number commonly used to characterize a set of data is the arithmetic mean, frequently called the average, or just the mean. |

Median | The value exactly in the middle of an ordered set of numbers is the median. |

Mode | The mode of a set of data is the number that appears most frequently, if there is one, but the mode does not have to be in any way a measure of central tendency. |

Mean absolute deviation (MAD) | The mean absolute deviation (MAD) makes use of the absolute value to find the distance each data point is away from the mean. Then the mean of those distances is found to give an “average distance from the mean” for each of the points. |

Standard deviation | The standard deviation, s, of n numbers is the square root of the variance, v. |

Normal curve | A normal curve is a smooth, bell-shaped curve that depicts frequency values distributed symmetrically about the mean. |

Percentile | A percentile shows a person’s score relative to other scores. Percentiles divide the set of data into 100 equal parts. |

Decile | Deciles are points that divide a distribution into 10 equally spaced sections. |

Created by:
marianhood