Relate Measures to Distribution Shape - 6th Grade Math
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What is the formula for the interquartile range?
What is the formula for the interquartile range?
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$IQR = Q_3 - Q_1$. Difference between third and first quartiles.
$IQR = Q_3 - Q_1$. Difference between third and first quartiles.
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Which measure of variability is typically paired with the mean for symmetric data?
Which measure of variability is typically paired with the mean for symmetric data?
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Mean absolute deviation (MAD). MAD averages distances from mean for symmetric data.
Mean absolute deviation (MAD). MAD averages distances from mean for symmetric data.
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Which measure of variability is typically paired with the median for skewed data?
Which measure of variability is typically paired with the median for skewed data?
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Interquartile range (IQR). IQR measures middle 50% spread, ignoring extremes.
Interquartile range (IQR). IQR measures middle 50% spread, ignoring extremes.
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Identify the distribution shape that best supports using mean and MAD as a summary.
Identify the distribution shape that best supports using mean and MAD as a summary.
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Approximately symmetric with no outliers. Mean and MAD assume no skew or extreme values.
Approximately symmetric with no outliers. Mean and MAD assume no skew or extreme values.
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Which context is more likely to need median and IQR: test scores or home prices?
Which context is more likely to need median and IQR: test scores or home prices?
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Home prices. Home prices often have luxury outliers creating skew.
Home prices. Home prices often have luxury outliers creating skew.
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A data set is symmetric with no outliers; which variability measure is more appropriate?
A data set is symmetric with no outliers; which variability measure is more appropriate?
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MAD. MAD works best with symmetric, clean data.
MAD. MAD works best with symmetric, clean data.
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A data set is symmetric but has one very high outlier; which center is more appropriate?
A data set is symmetric but has one very high outlier; which center is more appropriate?
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Median. One outlier disrupts mean despite symmetry.
Median. One outlier disrupts mean despite symmetry.
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Choose the better variability measure for data with an extreme value: MAD or IQR?
Choose the better variability measure for data with an extreme value: MAD or IQR?
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IQR. IQR focuses on middle 50%, ignoring extremes.
IQR. IQR focuses on middle 50%, ignoring extremes.
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Choose the better center for data with an extreme value: mean or median?
Choose the better center for data with an extreme value: mean or median?
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Median. Extreme values don't affect the middle position.
Median. Extreme values don't affect the middle position.
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Identify the best summary for a left-skewed distribution: mean and MAD or median and IQR.
Identify the best summary for a left-skewed distribution: mean and MAD or median and IQR.
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Median and IQR. Left skew means outliers pull mean left.
Median and IQR. Left skew means outliers pull mean left.
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Identify the best summary for a right-skewed distribution: mean and MAD or median and IQR.
Identify the best summary for a right-skewed distribution: mean and MAD or median and IQR.
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Median and IQR. Right skew means outliers pull mean right.
Median and IQR. Right skew means outliers pull mean right.
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What is the main reason the mean is not preferred when strong outliers are present?
What is the main reason the mean is not preferred when strong outliers are present?
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It is sensitive to outliers. Extreme values pull the mean toward them.
It is sensitive to outliers. Extreme values pull the mean toward them.
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What is the main reason the median is preferred when outliers are present?
What is the main reason the median is preferred when outliers are present?
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It is resistant to outliers. Outliers don't change the middle value's position.
It is resistant to outliers. Outliers don't change the middle value's position.
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Which measure of center is usually best for a skewed distribution or one with outliers?
Which measure of center is usually best for a skewed distribution or one with outliers?
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Median. The median is unaffected by extreme values in the tails.
Median. The median is unaffected by extreme values in the tails.
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Which measure of center is usually best for a roughly symmetric distribution with no outliers?
Which measure of center is usually best for a roughly symmetric distribution with no outliers?
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Mean. The mean uses all values equally, ideal for balanced data.
Mean. The mean uses all values equally, ideal for balanced data.
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Which choice is more appropriate for adult heights: mean and MAD, or median and IQR?
Which choice is more appropriate for adult heights: mean and MAD, or median and IQR?
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Mean and MAD. Heights follow a bell curve with few extremes.
Mean and MAD. Heights follow a bell curve with few extremes.
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Which choice is more appropriate for incomes in a city: mean and MAD, or median and IQR?
Which choice is more appropriate for incomes in a city: mean and MAD, or median and IQR?
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Median and IQR. Income data typically has high earners creating right skew.
Median and IQR. Income data typically has high earners creating right skew.
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What does the mean absolute deviation (MAD) measure in words?
What does the mean absolute deviation (MAD) measure in words?
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Typical distance from the mean. Average of absolute deviations from the mean.
Typical distance from the mean. Average of absolute deviations from the mean.
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What does $Q_3$ represent in a data set?
What does $Q_3$ represent in a data set?
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The third quartile (about the $75$th percentile). 75% of data falls below this value.
The third quartile (about the $75$th percentile). 75% of data falls below this value.
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What does $Q_1$ represent in a data set?
What does $Q_1$ represent in a data set?
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The first quartile (about the $25$th percentile). 25% of data falls below this value.
The first quartile (about the $25$th percentile). 25% of data falls below this value.
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What does the IQR measure in a data set?
What does the IQR measure in a data set?
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Spread of the middle $50%$ of the data. IQR captures the range containing the central half.
Spread of the middle $50%$ of the data. IQR captures the range containing the central half.
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State the formula for interquartile range in terms of quartiles.
State the formula for interquartile range in terms of quartiles.
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$\text{IQR}=Q_3-Q_1$. Subtract first quartile from third quartile.
$\text{IQR}=Q_3-Q_1$. Subtract first quartile from third quartile.
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Identify the better summary for a skewed data set: “mean and MAD” or “median and IQR.”
Identify the better summary for a skewed data set: “mean and MAD” or “median and IQR.”
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Median and IQR. Skewed data requires outlier-resistant measures.
Median and IQR. Skewed data requires outlier-resistant measures.
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What measure of center is most appropriate for a symmetric distribution with no outliers?
What measure of center is most appropriate for a symmetric distribution with no outliers?
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Mean. Mean works best when data is balanced around the center.
Mean. Mean works best when data is balanced around the center.
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What measure of center is most appropriate for a skewed distribution with outliers?
What measure of center is most appropriate for a skewed distribution with outliers?
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Median. Median resists the pull of extreme values in skewed data.
Median. Median resists the pull of extreme values in skewed data.
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