Statistics of One Variable

Statistics of One Variable

1. Graphs

   • Frequency Tables: A Frequency Table is a table that lists items and uses tally marks to record and show the number of times they occur.
   • Histogram: A bar graph in which the areas of the bars are proportional to the frequencies for various values of the variable.
   • Bar graph: A chart or diagram that represents quantities with horizontal or vertical bars whose lengths are proportional to the quantities
   • Circle Graph: A graph that represents quantities with segments of a circle that are proportional to the quantities. Circle graphs are also called pie charts.
   • Pictograph: A chart or diagram that represents quantities with symbols.
   • Box-and-whisker plot: A graph that summarizes a set of data by representing the first quartile, the median, and the third quartile with a box and, the lowest and highest data with the ends of lines extending from the box.

2. Variables

   • Variable: A quantity that can have any set of values
   • Continuous Variable: Involving a variable or data that can have an infinite number of possible values in a given interval. A continuous function or distribution that can be graphed as a smooth curve.
   • Discrete Variable: A variable that can take on only certain values within a given range.

3. Frequency

   • Frequency Diagram: A diagram such as a histogram or frequency polygon, that shows the frequencies with which different values of a variable occur
   • Frequency Polygon: A plot of frequencies versus variables values with the resulting points joined by line segments.
   • Relative Frequency Polygon: The frequency of a value or group of values expressed as a fraction or percent of the whole data set
   • Cumulative Frequency Polygon: A graph that shows the running total of the frequencies for values of the variable starting from the lowest value

4. Data

   • Raw Data: Unprocessed information.
   • Classes or Intervals: A set of data whose values lie within a given range or interval/ a set of all numbers between two given numbers
   • Categorical Data: Data that can be sorted or divided by type rather than by numerical values.
   • Consumer Price Index (CPI): A collective measure of the cost of items purchased by a typical family.
   • Inflation: An increase in the overall price of goods and services.
   • Measures of central tendency: The values around which a set of the data tends to cluster.
   • Mean: The sum of the values in a set of data divided by the number of values.
   • Median: The middle value of a set of data ranked from highest to lowest. If there is an odd number of data, the median is the midpoint between the two middle values.
   • Mode: The value in a distribution or set of data that occurs most frequently.
   • Outliers: Points in a set of data that are significantly far from the majority of the other data.
   • Measures of spread: Quantities that indicate how closely a set of data clusters around its central values.

5. Sample

   • Sample: A group of items or people selected from a population.
   • Simple Random Sample: A sample in which every member of a population has an equal and independent chance of being selected.
   • Systemic Sample: A statistical method involving the selection of elements from an ordered sampling frame.
   • Stratified sample: A sample in which each stratum or group is represented in the same proportion as it appears in the population.
   • Cluster sampling: A survey of selected groups within a population. This sampling technique can save time and expense, but may not give reliable results unless the clusters are representative of the population.
   • Multistage Sampling: Multistage Sampling is a sampling strategy (e.g., gathering participants for a study) used when conducting studies involving a very large population. The entire population is divided into naturally-occurring clusters and sub-clusters, from which the researcher randomly selects the sample.
   • Voluntary-response sample: A sampling technique in which participation is at the discretion or initiative of the respondent.
   • Convenience sample: A sample selected simply because it is easily accessible. Such samples may not be random, so their results are not always reliable.

6. Bias

   • Sampling bias: Bias resulting from a sampling frame that does not reflect the characteristics of the population.
   • Non-response bias: Bias occurring when particular groups are under-represented in a survey because they choose not to participate.
   • Measurement bias: Bias resulting from a data collection method that consistently either under- or over-estimates a characteristic of the population.
   • Response bias: Bias that occurs when participants in a survey deliberately give false or misleading answers.

7. Formulas and Range

   • Range: The difference between the highest and lowest values in a set of data.
   • Index: A number relating the value of a variable, or groups of variables, to a base level, which is often the value of particular date.
   • Standard deviation: The square root of the mean of the squares of the deviations of a set of data.
   • Variance: The mean of the squares of the deviations for a set of data. Variance is denoted by σ2 for a population and s2 for a sample.
   • Quartile: A statistical term describing a division of observations into four defined intervals based upon the values of the data and how they compare to the entire set of observations.
   • Interquartile range: The range of the central half of a set of data when the data are arranged in numerical order.
   • Semi-interquartile range: One half of the interquartile range.