Give Measures of Center and Variability - 6th Grade Math
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What is the median of an ordered data set with an even number of values?
What is the median of an ordered data set with an even number of values?
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Average of the two middle values. With even count, median is between the two center values.
Average of the two middle values. With even count, median is between the two center values.
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What is the median of an ordered data set with an odd number of values?
What is the median of an ordered data set with an odd number of values?
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The middle value. With odd count, the median is the single center value.
The middle value. With odd count, the median is the single center value.
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Find the median of the ordered data set $1, 4, 6, 10$.
Find the median of the ordered data set $1, 4, 6, 10$.
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$5$. $\frac{4+6}{2} = \frac{10}{2} = 5$ (average of middle two).
$5$. $\frac{4+6}{2} = \frac{10}{2} = 5$ (average of middle two).
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Which description best indicates a striking deviation: a value far from the rest or a value near the center?
Which description best indicates a striking deviation: a value far from the rest or a value near the center?
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A value far from the rest (an outlier). Outliers are striking deviations from the pattern.
A value far from the rest (an outlier). Outliers are striking deviations from the pattern.
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A data set has $Q_1=12$ and $Q_3=20$. What is the IQR?
A data set has $Q_1=12$ and $Q_3=20$. What is the IQR?
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$8$. $\text{IQR} = Q_3 - Q_1 = 20 - 12 = 8$.
$8$. $\text{IQR} = Q_3 - Q_1 = 20 - 12 = 8$.
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A data set has mean $10$. What is $|x-\bar{x}|$ when a value is $x=6$?
A data set has mean $10$. What is $|x-\bar{x}|$ when a value is $x=6$?
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$4$. Absolute deviation = $|6-10| = 4$.
$4$. Absolute deviation = $|6-10| = 4$.
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Find the MAD for the data set $1, 2, 3$ (use mean absolute deviation from the mean).
Find the MAD for the data set $1, 2, 3$ (use mean absolute deviation from the mean).
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$\frac{2}{3}$. Mean is $2$; deviations: $1,0,1$; MAD = $\frac{2}{3}$.
$\frac{2}{3}$. Mean is $2$; deviations: $1,0,1$; MAD = $\frac{2}{3}$.
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Find the IQR for the ordered data set $2, 3, 5, 8, 9, 10, 12, 15$.
Find the IQR for the ordered data set $2, 3, 5, 8, 9, 10, 12, 15$.
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$7$. $Q_3 - Q_1 = 11 - 4 = 7$ (from previous quartiles).
$7$. $Q_3 - Q_1 = 11 - 4 = 7$ (from previous quartiles).
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Identify $Q_1$ for the ordered data set $2, 3, 5, 8, 9, 10, 12, 15$.
Identify $Q_1$ for the ordered data set $2, 3, 5, 8, 9, 10, 12, 15$.
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$4$. Median of lower half: ${2,3,5,8}$ is $\frac{3+5}{2}=4$.
$4$. Median of lower half: ${2,3,5,8}$ is $\frac{3+5}{2}=4$.
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Find the median of the ordered data set $3, 7, 9, 12, 20$.
Find the median of the ordered data set $3, 7, 9, 12, 20$.
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$9$. Middle value of 5 ordered values is the 3rd one.
$9$. Middle value of 5 ordered values is the 3rd one.
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Find the mean of the data set $2, 4, 6, 8$.
Find the mean of the data set $2, 4, 6, 8$.
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$5$. $\frac{2+4+6+8}{4} = \frac{20}{4} = 5$
$5$. $\frac{2+4+6+8}{4} = \frac{20}{4} = 5$
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Which measure of center is more resistant to outliers: mean or median?
Which measure of center is more resistant to outliers: mean or median?
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Median. Outliers affect mean but not median position.
Median. Outliers affect mean but not median position.
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What does a larger MAD indicate about a data set compared to a smaller MAD?
What does a larger MAD indicate about a data set compared to a smaller MAD?
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Values are farther from the mean on average. Larger MAD means data is more spread out.
Values are farther from the mean on average. Larger MAD means data is more spread out.
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What does a larger IQR indicate about a data set compared to a smaller IQR?
What does a larger IQR indicate about a data set compared to a smaller IQR?
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Greater variability in the middle $50%$. Larger IQR means more spread in the middle half.
Greater variability in the middle $50%$. Larger IQR means more spread in the middle half.
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What is the mean absolute deviation (MAD) from the mean $\bar{x}$ for $n$ values?
What is the mean absolute deviation (MAD) from the mean $\bar{x}$ for $n$ values?
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$\text{MAD} = \frac{\sum |x-\bar{x}|}{n}$. Average distance of data points from the mean.
$\text{MAD} = \frac{\sum |x-\bar{x}|}{n}$. Average distance of data points from the mean.
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What does $Q_3$ represent in an ordered data set?
What does $Q_3$ represent in an ordered data set?
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Median of the upper half of the data. Third quartile: 75% of data falls below this value.
Median of the upper half of the data. Third quartile: 75% of data falls below this value.
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What does $Q_1$ represent in an ordered data set?
What does $Q_1$ represent in an ordered data set?
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Median of the lower half of the data. First quartile: 25% of data falls below this value.
Median of the lower half of the data. First quartile: 25% of data falls below this value.
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What is the interquartile range (IQR) in terms of quartiles $Q_1$ and $Q_3$?
What is the interquartile range (IQR) in terms of quartiles $Q_1$ and $Q_3$?
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$\text{IQR} = Q_3 - Q_1$. Measures spread of the middle 50% of data.
$\text{IQR} = Q_3 - Q_1$. Measures spread of the middle 50% of data.
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What does a larger IQR tell you about a data set compared to a smaller IQR?
What does a larger IQR tell you about a data set compared to a smaller IQR?
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The middle $50%$ of the data are more spread out. Larger IQR means greater spread in the middle half.
The middle $50%$ of the data are more spread out. Larger IQR means greater spread in the middle half.
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What is the median of a data set after the values are put in order?
What is the median of a data set after the values are put in order?
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The middle value, or the mean of the two middle values. For odd count, take middle; for even, average the two middle values.
The middle value, or the mean of the two middle values. For odd count, take middle; for even, average the two middle values.
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What is the interquartile range (IQR) in terms of $Q_1$ and $Q_3$?
What is the interquartile range (IQR) in terms of $Q_1$ and $Q_3$?
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$\text{IQR}=Q_3-Q_1$. Measures spread of the middle 50% of data.
$\text{IQR}=Q_3-Q_1$. Measures spread of the middle 50% of data.
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What is the mean absolute deviation (MAD) from the mean for values $x_1,\dots,x_n$?
What is the mean absolute deviation (MAD) from the mean for values $x_1,\dots,x_n$?
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$\text{MAD}=\frac{|x_1-\bar{x}|+\cdots+|x_n-\bar{x}|}{n}$. Average distance of all values from the mean.
$\text{MAD}=\frac{|x_1-\bar{x}|+\cdots+|x_n-\bar{x}|}{n}$. Average distance of all values from the mean.
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Identify the striking deviation (outlier) in the data set $4,5,5,6,6,7,30$.
Identify the striking deviation (outlier) in the data set $4,5,5,6,6,7,30$.
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$30$. Much larger than other values ($4-7$).
$30$. Much larger than other values ($4-7$).
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What does a larger MAD tell you about a data set compared to a smaller MAD?
What does a larger MAD tell you about a data set compared to a smaller MAD?
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Values are farther from the mean on average (more variability). Larger MAD indicates data points deviate more from center.
Values are farther from the mean on average (more variability). Larger MAD indicates data points deviate more from center.
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Which measure of center is usually more resistant to outliers: mean or median?
Which measure of center is usually more resistant to outliers: mean or median?
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Median. Outliers don't affect the middle position value.
Median. Outliers don't affect the middle position value.
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