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

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.

  • The Regression Method

    • The average SAT score is 560, with a standard deviation of 75.
    • The average first year GPA is 2.8, with a standard deviation of 0.5.
    • With no other information given, it is best to predict using the average.
    • Instead of just predicting 2.8, this time we look at the graph of averages and predict her GPA is whatever the average is of all the students in our sample who also scored a 680 on the SAT.
    • If you know the independent variable, or $x$-value (you know the SAT score), the best prediction of the dependent variable, or $y$-value (in this case, the GPA), is the average of all the $y$-values for that specific $x$-value.

  • 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?

  • 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 of a Single Mean and Single Proportion

    • In a recent survey, it was stated that Americans watch television on average four hours per day.
    • Draw a graph and label it appropriately.Shade the actual level of significance. 6.1.
    • Graph: 6.2.
    • Draw a graph and label it appropriately.Shade the actual level of significance. a.
    • Graph: b.

  • 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.

  • 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.

  • Homework

    • Sketch and label a graph of the distribution.
    • Sketch and label a graph of the distribution.
    • Suppose that the length of long distance phone calls, measured in minutes, is known to have an exponential distribution with the average length of a call equal to 8 minutes.
    • On average, how long would you expect 1 car battery to last?
    • The average lifetime of a certain new cell phone is 3 years.

  • Practice 1: Uniform Distribution

    • The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years.
    • Height of the rectangle: 1.4.
    • Exercise 5.6.11: Find the average age of the cars in the lot.
    • Exercise 5.6.12: Find the third quartile of ages of cars in the lot.
    • Solutions to problems can be found at the end of the chapter

  • Practice 3: Test of a Single Variance

    • Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes.
    • The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.
    • Graph the situation.
    • If an additional test were done on the claim of the average delay, which distribution would you use?
    • If an additional test was done on the claim of the average delay, but 45 flights were surveyed, which distribution would you use?