9 Questions
Explain the behavior of the Arithmetic Mean (AM) and the Harmonic Mean (HM) in comparison to the Geometric Mean (GM).
The AM is dominated by large values, while the HM gives more weight to smaller values. The GM gives equal weight to all values in the data set.
How does the Geometric Mean (GM) respond to changes in data values?
The GM gives equal weight to all values in the data set, so a change in value by a certain percentage results in the same change in the GM.
How does the Arithmetic Mean (AM) and the Geometric Mean (GM) differ in their response to changes in the data set?
The AM is dominated by large values, while the GM gives equal weight to all values in the data set, resulting in a consistent response to changes in the data values.
What effect does a 10% change in the largest value have on the Arithmetic Mean (AM) compared to the Geometric Mean (GM)?
A 10% change in the largest value has a noticeable effect on the AM, while it has the same effect on the GM as a 10% change in any of the data values.
What are the limitations of using measures such as MIPS and MFLOPS to evaluate processor performance?
Differences in instruction sets and the execution rate not being a valid means of comparison.
Why did industry and academic interest shift to measuring the performance of systems using a set of benchmark programs in the late 1980s and early 1990s?
To provide guidance to customers trying to decide which system to buy, and to be useful to vendors and designers in determining how to design systems to meet benchmark goals.
How do benchmarks provide guidance to customers trying to decide which system to buy?
By allowing the same set of programs to be run on different machines and the execution times compared.
What are the desirable characteristics of a benchmark program according to [WEIC90]?
- Written in a high-level language for portability. 2. Representative of a particular kind of programming domain or paradigm. 3. Easily measurable. 4. Widely distributed.
Why is the performance of a given processor on a given program not always useful in determining its performance on a very different type of application?
Due to the differences in how processors handle different types of applications.
Study Notes
Means in Statistics
- Arithmetic Mean (AM) is sensitive to outliers and skewed data, whereas Geometric Mean (GM) is more robust to extreme values.
- Harmonic Mean (HM) is used for averaging rates and ratios, and it is biased towards the smaller values.
Geometric Mean (GM)
- GM responds to changes in data values by becoming smaller as the variability in the data increases.
- GM is more suitable for data that has a multiplicative effect, such as rates of change.
Comparison of Arithmetic Mean (AM) and Geometric Mean (GM)
- AM is sensitive to changes in the data set, as it is affected by extreme values, whereas GM is more resistant to such changes.
- A 10% change in the largest value has a significant impact on the AM, whereas it has a relatively smaller effect on the GM.
Limitations of MIPS and MFLOPS
- Measuring processor performance using MIPS (Millions of Instructions Per Second) and MFLOPS (Millions of Floating-Point Operations Per Second) is limited, as it does not account for other factors that affect performance, such as memory access and I/O operations.
Shift to Benchmarking
- Industry and academic interest shifted to measuring system performance using benchmark programs in the late 1980s and early 1990s, as it provided a more comprehensive and realistic evaluation of system performance.
Benchmarking
- Benchmarks provide guidance to customers by giving them a standardized way to compare the performance of different systems.
- A benchmark program is designed to mimic real-world applications and provide a realistic evaluation of system performance.
Desirable Characteristics of a Benchmark Program
- According to [WEIC90], a good benchmark program should have the following characteristics: portability, scalability, and relevance to real-world applications.
Limitations of Processor Performance
- The performance of a processor on a given program is not always indicative of its performance on a very different type of application, due to the varying demands of different applications.
Test your understanding of the geometric mean with this quiz. Explore how the geometric mean behaves in comparison to other types of means, and gain intuitive insights into its characteristics.
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