graph of averages

(noun)

a plot of the average values of one variable (say $y$) for small ranges of values of the other variable (say $x$), against the value of the second variable ($x$) at the midpoints of the ranges

Related Terms

  • extrapolation
  • interpolation

Examples of graph of averages in the following topics:

  • A Graph of Averages

    • A graph of averages and the least-square regression line are both good ways to summarize the data in a scatterplot.
    • Sometimes, a graph of averages is used to show a pattern between the $y$ and $x$ variables.
    • In a graph of averages, the $x$-axis is divided up into intervals.
    • The points on a graph of averages do not usually line up in a straight line, making it different from the least-squares regression line.
    • The graph of averages plots a typical $y$ value in each interval: some of the points fall above the least-squares regression line, and some of the points fall below that line.
  • Clustering

    • The average distance between pairs of actors in large empirical networks are often much shorter than in random graphs of the same size.
    • That is, the density in local neighborhoods of large graphs tend to be much higher than we would expect for a random graph of the same size.
    • The "small world" phenomena -- a combination of short average path lengths over the entire graph, coupled with a strong degree of "clique-like" local neighborhoods -- seems to have evolved independently in many large networks.
    • The average geodesic distance between all actors in a graph gets at the idea of how close actors are together.
    • The "overall" graph clustering coefficient is simply the average of the densities of the neighborhoods of all of the actors.
  • Lab 1: Central Limit Theorem (Pocket Change)

    • Sketch the graph using a ruler and pencil.
    • Record the values of the average of their change.
    • Sketch the graph using a ruler and pencil.
    • Record the values of the average of their change.
    • In the section titled "Collecting Averages of Groups of Five", what was the approximate distribution of the averages?
  • Aggregate Production

    • The average physical product is at its maximum.
    • Stage 2: output increases at a decreasing rate and the average and marginal physical product are declining.
    • The average product of fixed inputs are still rising.
    • The production function of a firm or economy can be graphed using the total, average, and marginal products.
    • The aggregate production is determined based on the stages of production and the results of the graph.
  • The Law of Diminishing Returns

    • This increase in the marginal cost of output as production increases can be graphed as the marginal cost curve, with quantity of output on the x axis and marginal cost on the y axis.
    • The average total cost of production is the total cost of producing all output divided by the number of units produced.
    • Average total cost is interpreted as the the cost of a typical unit of production.
    • Average total cost can also be graphed with quantity of output on the x axis and average cost on the y-axis.
    • As long as the marginal cost of production is lower than the average total cost of production, the average cost is decreasing.
  • Homework

    • Sketch the distributions of X and $\bar{X}$ on the same graph.
    • Graph the situation and shade in the area to be determined.
    • Graph the situation and shade in the area to be determined.
    • Sketch the graph.
    • Does this histogram look like the graph in (3)?
  • Lab: Hypothesis Testing for Two Means and Two Proportions

    • Draw a graph and label it appropriately.
    • Draw a graph and label it appropriately.
    • Draw a graph and label it appropriately.
    • Test whether women have, on average, more pairs of shoes than men.
    • Draw a graph and label it appropriately.
  • Average and Marginal Cost

    • The average cost is the total cost divided by the number of goods produced.
    • It is also equal to the sum of average variable costs and average fixed costs.
    • Average costs are the driving factor of supply and demand within a market.
    • Short run average costs vary in relation to the quantity of goods being produced.
    • This graph is a cost curve that shows the average total cost, marginal cost, and marginal revenue.
  • Exercises

    • Which of the box plots on the graph has a large positive skew?
    • (PR) Plot histograms of the time spent with the average-weight and overweight patients.
    • (AT) Create a line graph of the data.
    • (SG) Create histograms and stem and leaf displays of both high-school grade point average and university grade point average.
    • For the graph below, of heights of singers in a large chorus.
  • Comparing Marginal and Average Tax Rates

    • Taxes can be evaluated based on an average impact or a marginal impact and can be categorized as progressive, regressive, or proportional.
    • An average tax rate is the ratio of the total amount of taxes paid, T, to the total tax base, P, (taxable income or spending), expressed as a percentage.
    • A regressive tax is a tax imposed in such a manner that the average tax rate decreases as the amount subject to taxation increases .
    • The amount of the tax is in proportion to the amount subject to taxation.
    • Graph demonstrates a progressive tax distribution on income that becomes regressive for top earners.
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