Statistics/Summary/Averages/Moving Average

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Statistics


  1. Introduction
    1. What Is Statistics?
    2. Subjects in Modern Statistics
    3. Why Should I Learn Statistics? 0% developed
    4. What Do I Need to Know to Learn Statistics?
  2. Different Types of Data
    1. Primary and Secondary Data
    2. Quantitative and Qualitative Data
  3. Methods of Data Collection
    1. Experiments
    2. Sample Surveys
    3. Observational Studies
  4. Data Analysis
    1. Data Cleaning
    2. Moving Average
  5. Summary Statistics
    1. Measures of center
      1. Mean, Median, and Mode
      2. Geometric Mean
      3. Harmonic Mean
      4. Relationships among Arithmetic, Geometric, and Harmonic Mean
      5. Geometric Median
    2. Measures of dispersion
      1. Range of the Data
      2. Variance and Standard Deviation
      3. Quartiles and Quartile Range
      4. Quantiles
  6. Displaying Data
    1. Bar Charts
    2. Comparative Bar Charts
    3. Histograms
    4. Scatter Plots
    5. Box Plots
    6. Pie Charts
    7. Comparative Pie Charts
    8. Pictograms
    9. Line Graphs
    10. Frequency Polygon
  7. Probability
    1. Introduction to Probability
    2. Bernoulli Trials
    3. Introductory Bayesian Analysis
  8. Distributions
    1. Discrete Distributions
      1. Uniform Distribution
      2. Bernoulli Distribution
      3. Binomial Distribution
      4. Poisson Distribution
      5. Geometric Distribution
      6. Negative Binomial Distribution
      7. Hypergeometric Distribution
    2. Continuous Distributions
      1. Uniform Distribution
      2. Exponential Distribution
      3. Gamma Distribution
      4. Normal Distribution
      5. Chi-Square Distribution
      6. Student-t Distribution
      7. F Distribution
      8. Beta Distribution
      9. Weibull Distribution
  9. Testing Statistical Hypothesis
    1. Purpose of Statistical Tests
    2. Formalism Used
    3. Different Types of Tests
    4. z Test for a Single Mean
    5. z Test for Two Means
    6. t Test for a single mean
    7. t Test for Two Means
    8. One-Way ANOVA F Test
    9. z Test for a Single Proportion
    10. z Test for Two Proportions
    11. Testing whether Proportion A Is Greater than Proportion B in Microsoft Excel
    12. Spearman's Rank Coefficient
    13. Pearson's Product Moment Correlation Coefficient
    14. Chi-Squared Tests
      1. Chi-Squared Test for Multiple Proportions
      2. Chi-Squared Test for Contingency
    15. Approximations of distributions
  10. Point Estimates100% developed  as of 12:07, 28 March 2007 (UTC) (12:07, 28 March 2007 (UTC))
    1. Unbiasedness
    2. Measures of goodness
    3. UMVUE
    4. Completeness
    5. Sufficiency and Minimal Sufficiency
    6. Ancillarity
  11. Practice Problems
    1. Summary Statistics Problems
    2. Data-Display Problems
    3. Distributions Problems
    4. Data-Testing Problems
  12. Numerical Methods
    1. Basic Linear Algebra and Gram-Schmidt Orthogonalization
    2. Unconstrained Optimization
    3. Quantile Regression
    4. Numerical Comparison of Statistical Software
    5. Numerics in Excel
    6. Statistics/Numerical_Methods/Random Number Generation
  13. Multivariate Data Analysis
    1. Principal Component Analysis
    2. Factor Analysis for metrical data
    3. Factor Analysis for ordinal data
    4. Canonical Correlation Analysis
    5. Discriminant Analysis
  14. Analysis of Specific Datasets
    1. Analysis of Tuberculosis
  15. Appendix
    1. Authors
    2. Glossary
    3. Index
    4. Links

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Moving Average[edit]

A moving average is used when you want to get a general picture of the trends contained in a data set. The data set of concern is typically a so-called "time series", i.e a set of observations ordered in time. Given such a data set X, with individual data points x_{i}, a 2n+1 point moving average is defined as \bar{x_{i}}=\frac{1}{2n+1}\sum_{k=i-n}^{i+n}x_{k}, and is thus given by taking the average of the 2n points around x_{i}. Doing this on all data points in the set (except the points too close to the edges) generates a new time series that is somewhat smoothed, revealing only the general tendencies of the first time series.

The moving average for many time-based observations is often lagged. That is, we take the 10 -day moving average by looking at the average of the last 10 days. We can make this more exciting (who knew statistics was exciting?) by considering different weights on the 10 days. Perhaps the most recent day should be the most important in our estimate and the value from 10 days ago would be the least important. As long as we have a set of weights that sums to 1, this is an acceptable moving-average. Sometimes the weights are chosen along an exponential curve to make the exponential moving-average.