graph of averages

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.