Questions and Answers
What does it mean if a statistic is resistant?
Extreme values do not affect its value substantially.
Why does HUD use the median to report the average price of a home?
Because the data are skewed right.
Which measure of central tendency will likely be larger if a histogram indicates the data is skewed right, mean or median? Why?
The mean will likely be larger because extreme values in the right tail pull the mean in the direction of the tail.
A data set will always have exactly one mode.
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What was the mean price per ad slot if the total revenue is $132 million for 62 ad slots?
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Compute the mean, median, and mode cost of repair for crashes costing $432, $443, $466, and $223.
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What measure of central tendency best describes the center of the distribution?
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Why is the median resistant but the mean is not?
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What does the sum of the deviations about the mean always equal?
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What does the standard deviation measure in conjunction with the mean?
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Chebyshev's inequality applies to all distributions regardless of shape, while the empirical rule holds only for bell-shaped distributions.
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What makes the range less desirable than the standard deviation as a measure of dispersion?
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Who is relatively taller: a 75-inch man or a 70-inch woman?
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If the median in a boxplot is to the left of the center and the right whisker is substantially longer than the left whisker, what type of skewness does this indicate?
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Study Notes
Resistant Statistics
- A statistic is deemed resistant if it remains largely unaffected by extreme values in the dataset.
Housing Prices
- The U.S. Department of Housing and Urban Development (HUD) reports the median home price due to the skewed nature of housing data.
Data Distribution and Central Tendency
- In a right-skewed distribution, the mean is typically larger than the median, as higher extreme values influence the mean upwards.
Modes in Data
- A dataset can have zero, one, or multiple modes; it is not limited to exactly one mode.
Ad Slot Revenue
- The average price per ad slot sold at a sporting event is calculated as $2.1 million from total revenue of $132 million.
Insurance Repair Costs
- For four car crashes:
- Mean repair cost: $391
- Median repair cost: $437.5
- Mode: None (no repeating values)
Central Tendency Measures
- The mean is often the best descriptor for the "center" of a distribution.
Resistance of Median vs Mean
- The median is resistant to skewed data and does not get affected by extreme values, unlike the mean, which can be pulled by such values.
Deviations About the Mean
- The sum of all deviations from the mean in a dataset always totals zero.
Standard Deviation and Mean
- Standard deviation describes the spread of a bell-shaped distribution and works alongside the mean which indicates center.
Distribution Rules
- Chebyshev's inequality applies universally to all distribution shapes; in contrast, the empirical rule specifically applies only to normal (bell-shaped) distributions.
Range vs Standard Deviation
- The range is a less preferable measure of dispersion because it only considers the extreme observations, neglecting the overall data variability.
Relative Height Comparison
- A 75-inch man has a lower relative height z-score than a 70-inch woman, indicating the woman is relatively taller considering their heights and deviations from average.
Boxplot Interpretation
- In boxplots, a left-placed median within the box and a significantly longer right whisker indicate a right-skewed distribution.
Studying That Suits You
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Description
Test your understanding of key concepts in Statistics Chapter 3 with these flashcards. Learn about resistant statistics and the use of median by HUD to represent skewed data. This is a great way to reinforce your knowledge on important statistical terms and their applications.
