## Statistics (Fach) / Statistics (Lektion)

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Statistics

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- Statistics A science dealing with the collection, analysis, interpretation, and presentation of numerical data.
- Population : A collection of persons, objects, or items under study.
- Census Gathering data from the entire population
- Sample A portion of the whole/ a subset of the population, must be large enough to represent the whole.
- Descriptive Statistics : Using data gathered on a group to describe or reach conclusions about the group.
- Inferential Statistics Data gathered from a sample and used to reach conclusions about the population from which the data was gathered (used to draw conclusions about the group or similar groups).
- Parameter Descriptive measure of the population, usually represented by Greek letters
- Statistic: Descriptive measure of a sample, usually represented by Roman letters
- Probability Statement Used to estimate the level of confidence in the probability statement.
- Nominal : In nominal measurement the numerical values just “name” the attribute uniquely. No ordering of the cases is implied. Numbers are used to classify or categorize, examples: Football shirt numbers ...
- Ordinal A variable is ordinal measureable if ranking is possible for values of the variable. Numbers are used to indicate rank or order, the relative magnitude of numbers if meaningful, but differences between ...
- Interval: In interval measurement the distance between attributes does have meaning. Distances between consecutive integers are equal, the relative magnitude of numbers if meaningful and differences between numbers ...
- Ratio In ratio measurement there is always an absolute zero that is meaningful. This means that you can construct a meaningful fraction (or ratio) with a ratio variable. In applied social research most “count” ...
- Parametric Statistics Requires that the data be interval or ratio.
- Non Parametric Statistics Used if data are nominal or ordinal, can also be used to analyse interval or ratio data.
- Ungrouped Data Have not been summarized in any way, are also called raw data.
- Grouped Data Have been organised into a frequency distribution
- frequency distribution summary of data presented in the form of class intervals and frequencies. Vary in shape and design and are constructed according to the individual researcher's preferences.
- Range Difference between the highest and the lowest numbers.
- Class midpoint/ class mark the midpoint of each class interval.
- Relative frequency The proportion of the total frequency that is in any given class interval in a frequency distribution.
- Cumulative frequency A running total of frequencies through the classes of a frequency distribution.
- Histogram A vertical bar chart where the area of each bar is equal the the frequency of the corresponding interval.
- Frequency Polygon A line graph of frequencies constructed by plotting a dot for the frequencies at the class midpoints and connecting the dots.
- Ogive A line graph of cumulative frequencies/ a cumulative frequency polygon which is plotted by graphing a dot at each class endpoint for the cumulative frequency value and connecting the dots.
- Pie chart a proportional representation for categories of a whole / a circular display of data where the area of the whole pie represents 100 % of the data being studied and slices represent a percentage breakdown ...
- Stem and Leaf Plot A graphical method of displaying data by separating each number into two groups, a stem and a leaf. The leftmost digits are the stems and the rightmost digits are the leaves.
- Pareto Chart A type of chart which contains both bars and a line graph. The bars display the values in descending order and the line graph shows the cumulative totals of each category, left to right. The purpose is ...
- Scatter plot A type of display using Cartesian coordinates to display values for two variables for a set of data. The data is displayed as a collection of points, each having the value of one variable determining ...
- Measures of Central Tendency Measures of central tedency yield information about "particular places or locations in a group of numbers". Common measures for ungrouped data are the mode, the median, the mean, percentiles and quartiles. ...
- Mode (Ungrouped) The most frequently occuring value in a data set. It is applicable to all levels of data measurement and can be used to determine what categories occur most frequently.
- Bimodal In a tie for the most frequently occuring value, two modes are listed.
- Multimodal Data sets that contain more than two modes
- Median (Ungrouped) The middle value in an ordered array of numbers applicable to ordinal, interval and ratio data.
- Mean (Ungrouped) the average of a group of numbers, applicable to interval and ratio data. It is affected by each value in the data set, including extreme values.
- Percentiles Measures of central tendency that divide a group of data into 100 parts. At least n % of the data lie below the nth percentile, and at most (100 - n) % lie above the nth percentile.
- Quartiles Measures of central tendency that divide a group of data into four subgroups
- Measures of Variability Tools that describe the spread or the dispersion of a set of data. Provide more meaningful data when used with measures of central tendency. Common measures of variability for ungrouped data are the range, ...
- Interquartile Range: Range of values between the first and third quartiles, thus the range of the "middle half" / middle 50%. Useful when researchers are interested in the middle 50 % and not the extremes.
- Mean Absolute Deviation The average of the absolute deviations from the mean, applicable to interval and ratio data.
- Variance The average of the squared deviations from the arithmetic mean, applicable to interval and ratio data. Population variance is denoted by a σ2 and sample variance is denoted by a S².
- Sum of Squared Deviations (SSD) SSD about the mean of a set of values (called Sum of Squares of X) is used throughout the book
- Standard Deviation The square root of the variance
- Empirical Rule A guideline that states the approximate % of values that fall within a given number of standard deviations of a mean of a set of data that are normally distributed (bell shaped)
- Chebyshev's Theorem States that at least 1 - 1 / k² values fall within + or - k standard deviations of the mean, regardless of the shape of the distribution. Thus it applies to all distributions.
- Z Score Represents the number of standard deviations a value (x) is above or below the mean of a set of numbers when the data are normally distributed. It allows the translation of a value's raw distrance from ...
- Coefficient of Variation The ratio of the standard deviation to the mean, expressed as a percentage. It is useful when comparing standard deviation computed from data with different means. It is a measurement of relative dispersion ...
- Mean (Grouped) The midpoint of each class interval is used to represent all the values in a class interval. The midpoint is weighted by the frequency of values in the class interval.
- Median (Grouped) The middle value in an ordered array of numbers.
- Mode (Grouped) The mode for grouped data is the class midpoint of the modal class. The modal class is the class interval with the greatest frequency.