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Statistics

Organizing and Representing Data

Data:

A description, usually in numerical form, of a property (or properties) of a population.

Dot plot:

A representation of data that uses dots above a number line to represent data values.

Stem-and-leaf plot:

A representation of data in which the first one or more digits of each data value constitute the stem and the remaining digits constitute the leaves..

Histogram:

A representation of data in which the height of the bar at a point on the number line represents the number of data points in an interval about the point or the relative frequency of the data in the interval..

Frequency:

The number of times a data vlaue appears in a data set..

Frequency of an interval:

The number of times a data value appears in a given interval along a number line..

Line graph:

A graph formed by joining data points..

Bar graph:

A histogram-like representation in which the bars are drawn above points on the horizontal axis corresponding to nonnumerical categories..

Pie chart:

A circle divided into sectors whose sizes (as measured by their angle) correspond to the percentages of a whole..

Pictograph:

A representation of data in which the frequency is indicated by icons chosen to bear some relationship to the data being represented..

Misleading representations:

Ways in which representations of data can be organized to confuse..

Additional resource:

http://www.andrews.edu/~calkins/math/edrm611 edrm02.htm.

Measuring the Center and Variation of Data

Central tendency:

Description in a number of ways (mean, median or mode) of the center of a data set.

Variability:

The spread of a data set, measured by the range, quartiles or the standard deviation of the data set..

Outlier:

A data value less than x - 1.5 X IQR or greater than x + 1.5 X IQR..

Box-and-whisker plot:

A representation summarized by five numbers (the least data value, Ql, median, Qu and the greatest data value..

Standard deviation:

A measure of the spread of the data in a sample. The standard formula for the standard deviation s is s = square root of (x1 - x) + (x2 - x) + ... + (xn - x)^2 / n, where x1, x2,..., xn are the n data values of the data set..

Mean:

The sum of the data values in a sample, divided by the number of data values..

Median:

The middle data value for a sample with an odd number of data values and the average of the two middle values for a sample with an even number of data values..

Mode:

A data value in a sample which appears as least as often as every other data point..

Range:

The difference between the greatest and least data values in a sample..

Midrange:

The average of the highest and lowest data points in a sample..

Quartiles:

Ql and Qu, are the points such that 25% of the data set does not exceed Ql and 25% of the data is not less than Qu..

Interquartile range:

IQR of a data set is the difference between the upper and lower quartile, or IQR = Ql - Qu..

Extremes:

The extremes of a data set are the least and greatest scores..

Uniform distribution:

A data set has a uniform distribution if every value has exactly the same number of data points..

Additional resource:

http://www.cliffsnotes.com/study_guide/Measures-of-Variability.topicArticleId-267532,articleId-267453.html.

Statistical Inference:

Population:. Sample:. Random sample:. Biased:. Relative frequency:. Distribution:. Normal distribution:. The 68-95-99.7 rule:. Random sequence of digits:. Random numbers:. Additional resource:. A particular set of objects about which information is desired.. A subset of the population.. A subset chosen from a population in such a way that every such subset of the same size has an equal chance of being chosen.. Biased data is selection criteria that systematically favor certain outcomes.. The frequency of the occurrence of a data value in a sample, expressed as a percentage.. A curve or histogram showing the relative frequency of the measurements of a characteristic of a population.. A special bell-shaped distribution valid for many populations.. In a normal distribution, 68% of the population lies within 1 standard deviation of the mean, 95% of the population lies within 2 standard deviations of the mean and 99.7% of the population lies within 3 standard deviations fo the mean.. A squence of digits chosen in such a way that, at each step, each digit has an equal chance of being chosen.. Numbers formed by successively choosing the appropriate digits from a random sequence of digits.. http://www.ghamsary.elac.org/Statistics_Chap01.pdf.