Questions and Answers
What does it mean if a statistic is resistant?
Extreme values do not affect its value substantially.
What is meant by the term 'resistant' in statistics?
A numerical summary of data that is not affected by extreme values.
Why does HUD use the median to report the average price of a home?
Because the data are skewed to the right.
If a histogram shows that the distribution of data is skewed right, which measure of central tendency will likely be larger, the mean or the median?
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What is the median?
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How is the mean calculated?
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What is the mode?
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What are the three measures of central tendency?
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What is the arithmetic mean?
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What is the population arithmetic mean?
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What is the sample arithmetic mean?
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What is the mean pH for tap water rounded to three decimal places based on the data provided?
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A data set will always have exactly one mode.
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Study Notes
Measures of Central Tendency
- A statistic is considered resistant if extreme values do not significantly impact its value.
- The median is often preferred over the mean for skewed data, as it provides a better representation of central tendency in these cases.
- The mean is calculated by summing all values in a data set and dividing by the number of observations, represented by the formula ( \bar{x} = \frac{x_1 + x_2 + ... + x_n}{n} ).
- The mode is the most frequently occurring value in a data set and can vary widely; a data set can have no mode, one mode, or multiple modes.
- The median is the middle value of a data set arranged in ascending order, denoted as "M."
- When data is skewed right (having extreme values on the high side), the mean is typically larger than the median due to these high values pulling the mean in their direction.
- Arithmetic Mean can refer to both sample and population means, calculated in the same fashion but distinguished by their scopes.
- The population arithmetic mean (µ) includes all individuals in the population and is a parameter, while the sample arithmetic mean (x̄) uses a subset of data and is considered a statistic.
- The acidity or alkalinity of solutions is measured by pH, with values below 7 indicating acidity and values above 7 indicating alkalinity.
- A single set of data may have multiple modes, may have no mode at all, or may have only one mode depending on the frequency of data values.
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Description
This quiz focuses on the concept of resistance in statistics, specifically related to measures of central tendency. It examines how extreme values impact statistical summaries and highlights the importance of resistant statistics. Test your understanding of these crucial statistical principles.
