range

(noun)

the length of the smallest interval which contains all the data in a sample; the difference between the largest and smallest observations in the sample

Related Terms

Examples of range in the following topics:

  • Range

    • The range is a measure of the total spread of values in a quantitative dataset.
    • In statistics, the range is a measure of the total spread of values in a quantitative dataset.
    • The mid-range is the midpoint of the range; as such, it is a measure of central tendency.
    • The mid-range also lacks robustness, as outliers change it significantly.
    • Interpret the range as the overall dispersion of values in a dataset

  • Measures of Variability

    • The range is 8.
    • What is the range?
    • Therefore, the range is 4.
    • Therefore the range is 6.
    • The semi-interquartile range is defined simply as the interquartile range divided by 2.

  • Interquartile Range

    • The interquartile range is equal to the difference between the upper and lower quartiles:
    • This is the Interquartile range, or IQR.
    • Unlike (total) range, the interquartile range has a breakdown point of 25%.
    • Thus, it is often preferred to the total range.
    • In other words, since this process excludes outliers, the interquartile range is a more accurate representation of the "spread" of the data than range.

  • The normal approximation breaks down on small intervals

    • Caution: The normal approximation may fail on small intervals The normal approximation to the binomial distribution tends to perform poorly when estimating the probability of a small range of counts, even when the conditions are met.
    • With such a large sample, we might be tempted to apply the normal approximation and use the range 69 to 71.
    • The tip to add extra area when applying the normal approximation is most often useful when examining a range of observations.

  • Student Learning Outcomes

    • Recognize, describe, and calculate the measures of the spread of data: variance, standard deviation, and range.

  • Introduction to confidence intervals

    • Instead of supplying just a point estimate of a parameter, a next logical step would be to provide a plausible range of values for the parameter.
    • This video introduces confidence intervals for point estimates, which are intervals that describe a plausible range for a population parameter.

  • Capturing the population parameter

    • A plausible range of values for the population parameter is called a confidence interval.
    • On the other hand, if we report a range of plausible values – a confidence interval – we have a good shot at capturing the parameter.

  • Properties of Pearson's r

    • A basic property of Pearson's r is that its possible range is from -1 to 1.

  • Finding the Area Under the Normal Curve

    • To calculate the probability that a variable is within a range in the normal distribution, we have to find the area under the normal curve.
    • To calculate the probability that a variable is within a range in the normal distribution, we have to find the area under the normal curve.
    • Interpret a $z$-score table to calculate the probability that a variable is within range in a normal distribution

  • The Regression Method

    • If the students admitted all had SAT scores within the range of 480 to 780, the regression model may not be a very good estimate for a student who only scored a 350 on the SAT.
    • Sometimes statisticians will use interpolation to predict data points within the range of known data points.
    • Extrapolation is also frequently used, in which data points beyond the known range of values is predicted.
    • An example of extrapolation, where data outside the known range of values is predicted.