Podcast
Questions and Answers
The calculation of the arithmetic mean is complex.
The calculation of the arithmetic mean is complex.
False
Every data set has only one arithmetic mean.
Every data set has only one arithmetic mean.
True
All the data in the data set are used to find the arithmetic mean.
All the data in the data set are used to find the arithmetic mean.
True
The arithmetic mean uses only some of the data in a data set.
The arithmetic mean uses only some of the data in a data set.
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The arithmetic mean can be used for further arithmetic treatment.
The arithmetic mean can be used for further arithmetic treatment.
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The arithmetic mean is the least affected by fluctuations of sampling.
The arithmetic mean is the least affected by fluctuations of sampling.
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The arithmetic mean will be truly reflective of the data set, if there are extreme values in the data set.
The arithmetic mean will be truly reflective of the data set, if there are extreme values in the data set.
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The arithmetic mean is highly influenced by outliers.
The arithmetic mean is highly influenced by outliers.
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Extreme values are always large values.
Extreme values are always large values.
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The arithmetic mean cannot be found by just inspection or through any diagrammatic presentation.
The arithmetic mean cannot be found by just inspection or through any diagrammatic presentation.
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The arithmetic mean can be accurately found if qualitative characteristics are under study.
The arithmetic mean can be accurately found if qualitative characteristics are under study.
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The arithmetic mean can be accurately found if the data is presented through unequal classes or through open-ended classes.
The arithmetic mean can be accurately found if the data is presented through unequal classes or through open-ended classes.
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The arithmetic mean is a suitable measure for statistical analysis in extremely skewed distributions.
The arithmetic mean is a suitable measure for statistical analysis in extremely skewed distributions.
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Study Notes
Merits of Arithmetic Mean
- Calculation is simple
- Unique value for each data set
- All data points in the set are used
- Represents the entire data set with a single value
- Suitable for further calculations
- Least affected by sampling fluctuations
Demerits of Arithmetic Mean
- Not truly representative if extreme values exist
- Example: Salaries of 5 siblings (10,000, 12,000, 7,000, 11,000, 65,000) = 21,000 (unrepresentative)
- Extreme values (outliers) can be high or low
- Example: Student's marks (90, 80, 85, 75, 20) = 70 (unrepresentative)
- Cannot be determined visually or diagrammatically
- Not suitable when data is qualitative
- Inappropriate for unequal or open-ended classes
- Not suitable for extremely skewed distributions
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Description
Explore the merits and demerits of the arithmetic mean in this detailed quiz. Learn how it can represent entire data sets and the limitations posed by extreme values or outliers. Test your understanding of this fundamental statistical concept.
