Let ​ Use a Riemann Sum with Four Subintervals

question 101

Multiple Choice

Let ​ Use a Riemann sum with four subintervals of equal length ( ) to approximate the area of R (under the graph of f on the interval [0, 2]) . Choose the representative points to be the left end points of the subintervals.
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Repeat previous part with eight subintervals of equal length ( ) .
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Compare the approximations obtained in previous parts with the exact area (14 sq units) . Do the approximations improve with larger n?
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• A) 12.25 sq units; 10.5 sq units; no
• B) 10.5 sq units; 12.25 sq units; no
• C) 10.5 sq units; 12.25 sq units; yes
• D) 12.25 sq units; 10.5 sq units; yes

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Definitions:

Variation

The difference in data set values from the mean, highlighting the dispersion or spread of a set of data points.

Quartile

A quartile is a type of statistical measure that divides a data set into four equal parts, revealing the spread and tendencies of the data.

Chebyshev's Theorem

A statistical rule stating for any real number k greater than one, at least (1-1/k^2) of the distribution's values lie within k standard deviations from the mean.

Standard Deviations

A metric indicating the degree of spread or variability in a collection of numbers, highlighting the distance of individual values from the central mean.