Midterm Glossary

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  • Statistics The science of collecting, organizing, analyzing, and interpreting numerical data for the purpose of making more effective decisions
  • 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.
  • 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 are gender (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 distance between $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. 
  • 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. 
  •  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. 
  • 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.
  • 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. 
  • Relative frequency distribution A frequency distribution that shows the fraction or proportion of the total observations in each class
  • 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 spread of a data set. The range, variance, and standard deviation are 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. 
  • 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.
  • 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.
  • Stem-and-leaf display A method to display a variable’s distribution using every value. Values are classified by the data’s 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.
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