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Exact Bounds on Sample Variance of Interval Data - Computer

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The document presents algorithms for calculating the lower and upper bounds of sample variance for interval data, addressing the challenges posed by incomplete information due to measurement errors. It introduces a quadratic-time algorithm to compute the exact lower bound of sample variance and discusses the NP-hard nature of computing the upper bound. The authors also propose efficient algorithms for specific practical scenarios where intervals do not intersect, highlighting the significance of interval arithmetic in statistical analysis.

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What are examples of data at the interval level?

Interval Data Examples Time of day in a 12-hour clock. Temperature in degrees Fahrenheit or Celsius (not Kelvin). IQ test. SAT and ACT scores. Age. Income range. Year. Voltage.

Is time an example of interval?

Some examples of variables that use interval scales would be time, temperature (Celsius), temperature (Fahrenheit), etc. When using a twelve hour clock, we can compare the time of 4:00 in the afternoon to 8:00 in the evening. It is possible to say that the difference in time is four hours (8:00 4:00).

What is an example of interval data?

Shared some examples of interval data: Temperature in Fahrenheit or Celsius, pH measure, IQ and SAT scores. Highlighted the descriptive statistics you can obtain using interval data: Frequency distribution, measures of central tendency (mode, median, and mean), and variability (range, standard deviation, and variance).

What is an example of a simple interval?

A simple interval (i.e., an interval smaller than or equal to an octave) may be inverted by raising the lower pitch an octave or lowering the upper pitch an octave. For example, the fourth from a lower C to a higher F may be inverted to make a fifth, from a lower F to a higher C.

What is the range of sample variance?

The range is the difference between the highest and lowest values in the data set. Variance is a measure of how far each value in a set of data is from the mean value. Variance is calculated by taking the average of the squared differences of each value from the mean.

What is an example of an interval type?

An interval consists of a set of fields. There is an implied ordering among the fields. For example, in a year-to-month interval, the year comes first, followed by the month. Similarly, in a day-to-minute interval, the fields are in the order day, hour, and minute.

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