Center, Shape, & Spread of Data - PSAT Math
Card 1 of 30
Identify the center line in a box plot: which statistic does it represent?
Identify the center line in a box plot: which statistic does it represent?
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Median. The box plot's center line shows the middle value.
Median. The box plot's center line shows the middle value.
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What is the outlier rule using $\text{IQR}$ (lower and upper fences)?
What is the outlier rule using $\text{IQR}$ (lower and upper fences)?
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Outliers are $<Q_1-1.5\text{IQR}$ or $>Q_3+1.5\text{IQR}$. Values beyond 1.5 IQRs from the quartiles.
Outliers are $<Q_1-1.5\text{IQR}$ or $>Q_3+1.5\text{IQR}$. Values beyond 1.5 IQRs from the quartiles.
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What is the median of a data set with an odd number of values?
What is the median of a data set with an odd number of values?
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The middle value after sorting the data. Sort first, then pick the one in the middle.
The middle value after sorting the data. Sort first, then pick the one in the middle.
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What is the mean of a data set in terms of the sum and number of values?
What is the mean of a data set in terms of the sum and number of values?
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$\text{mean}=\frac{\text{sum of values}}{\text{number of values}}$. Divide the total by how many values there are.
$\text{mean}=\frac{\text{sum of values}}{\text{number of values}}$. Divide the total by how many values there are.
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What is the median of a data set with an even number of values?
What is the median of a data set with an even number of values?
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The average of the two middle sorted values. No single middle value, so average the two center ones.
The average of the two middle sorted values. No single middle value, so average the two center ones.
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What does $Q_1$ represent in a sorted data set?
What does $Q_1$ represent in a sorted data set?
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The median of the lower half (the $25$th percentile). Splits the bottom 25% from the rest.
The median of the lower half (the $25$th percentile). Splits the bottom 25% from the rest.
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What does $Q_3$ represent in a sorted data set?
What does $Q_3$ represent in a sorted data set?
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The median of the upper half (the $75$th percentile). Splits the top 25% from the rest.
The median of the upper half (the $75$th percentile). Splits the top 25% from the rest.
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What is the mean of the data set $2,4,4,10$?
What is the mean of the data set $2,4,4,10$?
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$5$. $\frac{2+4+4+10}{4}=\frac{20}{4}=5$
$5$. $\frac{2+4+4+10}{4}=\frac{20}{4}=5$
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What is the median of the data set $3,7,8,12,20$?
What is the median of the data set $3,7,8,12,20$?
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$8$. Already sorted; middle of 5 values is the 3rd.
$8$. Already sorted; middle of 5 values is the 3rd.
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What is the median of the data set $1,5,6,10$?
What is the median of the data set $1,5,6,10$?
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$\frac{11}{2}$. Average of 5 and 6: $\frac{5+6}{2}=\frac{11}{2}$
$\frac{11}{2}$. Average of 5 and 6: $\frac{5+6}{2}=\frac{11}{2}$
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What is the range of the data set $-2,0,5,9$?
What is the range of the data set $-2,0,5,9$?
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$11$. $9-(-2)=11$
$11$. $9-(-2)=11$
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Given $Q_1=12$ and $Q_3=20$, what is the value of $\text{IQR}$?
Given $Q_1=12$ and $Q_3=20$, what is the value of $\text{IQR}$?
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$8$. $20-12=8$
$8$. $20-12=8$
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Given $Q_1=10$ and $\text{IQR}=6$, what is the lower outlier fence?
Given $Q_1=10$ and $\text{IQR}=6$, what is the lower outlier fence?
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$1$. $Q_1-1.5(\text{IQR})=10-1.5(6)=10-9=1$
$1$. $Q_1-1.5(\text{IQR})=10-1.5(6)=10-9=1$
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A distribution is right-skewed. Which is larger: mean or median?
A distribution is right-skewed. Which is larger: mean or median?
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Mean. The tail pulls the mean toward higher values.
Mean. The tail pulls the mean toward higher values.
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In a box plot, what does the length of the box (from $Q_1$ to $Q_3$) represent?
In a box plot, what does the length of the box (from $Q_1$ to $Q_3$) represent?
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The interquartile range, $\text{IQR}$. Shows the spread of the middle 50% of data.
The interquartile range, $\text{IQR}$. Shows the spread of the middle 50% of data.
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What is the interquartile range (IQR) in terms of quartiles?
What is the interquartile range (IQR) in terms of quartiles?
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$Q_3-Q_1$. Third quartile minus first quartile.
$Q_3-Q_1$. Third quartile minus first quartile.
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What is the mean of a data set with values $x_1, x_2, \dots, x_n$?
What is the mean of a data set with values $x_1, x_2, \dots, x_n$?
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$\frac{x_1+x_2+\cdots+x_n}{n}$. Sum all values and divide by the count.
$\frac{x_1+x_2+\cdots+x_n}{n}$. Sum all values and divide by the count.
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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 single middle value in the ordered list. With odd count, the middle value stands alone.
The single middle value in the ordered list. With odd count, the middle value stands alone.
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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, average the two center values.
Average of the two middle values. With even count, average the two center values.
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What is the mode of a data set?
What is the mode of a data set?
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The value that occurs most frequently. The value with the highest frequency.
The value that occurs most frequently. The value with the highest frequency.
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What is the range of a data set?
What is the range of a data set?
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$\text{max}-\text{min}$. Subtract the smallest value from the largest.
$\text{max}-\text{min}$. Subtract the smallest value from the largest.
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What is the five-number summary of a data set?
What is the five-number summary of a data set?
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$\text{min},\ Q_1,\ \text{median},\ Q_3,\ \text{max}$. Lists the key values that divide the data into quarters.
$\text{min},\ Q_1,\ \text{median},\ Q_3,\ \text{max}$. Lists the key values that divide the data into quarters.
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What is the standard deviation used to measure in a data set?
What is the standard deviation used to measure in a data set?
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Typical distance of values from the mean. Measures how spread out data points are.
Typical distance of values from the mean. Measures how spread out data points are.
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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 more than median.
Median. Outliers affect mean more than median.
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Which measure of spread is more resistant to outliers: range or $IQR$?
Which measure of spread is more resistant to outliers: range or $IQR$?
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$IQR$. IQR ignores extreme values, unlike range.
$IQR$. IQR ignores extreme values, unlike range.
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What is the outlier rule using $IQR$ for the lower fence?
What is the outlier rule using $IQR$ for the lower fence?
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Lower fence $=Q_1-1.5(IQR)$. Values below this are potential outliers.
Lower fence $=Q_1-1.5(IQR)$. Values below this are potential outliers.
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Identify the skew: if the mean is greater than the median, what is the distribution shape?
Identify the skew: if the mean is greater than the median, what is the distribution shape?
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Right-skewed (positively skewed). Tail extends right, pulling mean higher.
Right-skewed (positively skewed). Tail extends right, pulling mean higher.
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Identify the skew: if the mean is less than the median, what is the distribution shape?
Identify the skew: if the mean is less than the median, what is the distribution shape?
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Left-skewed (negatively skewed). Tail extends left, pulling mean lower.
Left-skewed (negatively skewed). Tail extends left, pulling mean lower.
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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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$5$. $(2+4+6+8)÷4=20÷4=5$.
$5$. $(2+4+6+8)÷4=20÷4=5$.
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Find the median of the data set $3,7,9,10,12$.
Find the median of the data set $3,7,9,10,12$.
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$9$. Middle value of ordered list is $9$.
$9$. Middle value of ordered list is $9$.
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