Interpreting Data Distributions and Outliers - Statistics
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What is the $IQR$ formula in terms of quartiles $Q_1$ and $Q_3$?
What is the $IQR$ formula in terms of quartiles $Q_1$ and $Q_3$?
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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 spread is more resistant to outliers: standard deviation or $IQR$?
Which measure of spread is more resistant to outliers: standard deviation or $IQR$?
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$IQR$. Based on quartiles, ignores extreme values.
$IQR$. Based on quartiles, ignores extreme values.
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Given $Q_1=10$, $Q_3=18$, what are the outlier fences using $1.5IQR$?
Given $Q_1=10$, $Q_3=18$, what are the outlier fences using $1.5IQR$?
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Lower $=-2$, upper $=30$. Lower: $10-1.5(8)=-2$; Upper: $18+1.5(8)=30$.
Lower $=-2$, upper $=30$. Lower: $10-1.5(8)=-2$; Upper: $18+1.5(8)=30$.
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Given fences $-2$ and $30$, is $x=31$ an outlier by the $1.5IQR$ rule (yes or no)?
Given fences $-2$ and $30$, is $x=31$ an outlier by the $1.5IQR$ rule (yes or no)?
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Yes, because $31>30$. Value exceeds upper fence of $30$.
Yes, because $31>30$. Value exceeds upper fence of $30$.
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Given $Q_1=10$, $Q_3=18$, what is $IQR$?
Given $Q_1=10$, $Q_3=18$, what is $IQR$?
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$8$. Apply formula: $IQR = 18 - 10 = 8$.
$8$. Apply formula: $IQR = 18 - 10 = 8$.
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In a boxplot, which part represents the $IQR$: the box, the whiskers, or the median line?
In a boxplot, which part represents the $IQR$: the box, the whiskers, or the median line?
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The box. Box spans from $Q_1$ to $Q_3$.
The box. Box spans from $Q_1$ to $Q_3$.
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Which summary is most appropriate for an approximately symmetric distribution with no outliers: mean and standard deviation, or median and $IQR$?
Which summary is most appropriate for an approximately symmetric distribution with no outliers: mean and standard deviation, or median and $IQR$?
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Mean and standard deviation. Non-resistant measures work well for clean data.
Mean and standard deviation. Non-resistant measures work well for clean data.
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Which summary is most appropriate for a skewed distribution with outliers: mean and standard deviation, or median and $IQR$?
Which summary is most appropriate for a skewed distribution with outliers: mean and standard deviation, or median and $IQR$?
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Median and $IQR$. Resistant measures handle outliers better.
Median and $IQR$. Resistant measures handle outliers better.
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Identify the effect of a single very large outlier on standard deviation (increase, decrease, or no change).
Identify the effect of a single very large outlier on standard deviation (increase, decrease, or no change).
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Increase. Outliers increase squared deviations from mean.
Increase. Outliers increase squared deviations from mean.
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Identify the effect of a single very large outlier on the median (large change or small change).
Identify the effect of a single very large outlier on the median (large change or small change).
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Small change (median is resistant). Median position barely shifts with one extreme value.
Small change (median is resistant). Median position barely shifts with one extreme value.
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Identify the effect of a single very large outlier on the mean (increase, decrease, or no change).
Identify the effect of a single very large outlier on the mean (increase, decrease, or no change).
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Increase. Large values pull mean upward in calculation.
Increase. Large values pull mean upward in calculation.
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Which option best describes a symmetric distribution: mean and median are about equal, or mean far from median?
Which option best describes a symmetric distribution: mean and median are about equal, or mean far from median?
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Mean and median are about equal. Balanced tails keep mean and median aligned.
Mean and median are about equal. Balanced tails keep mean and median aligned.
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If a distribution is left-skewed, what is the typical relationship between mean and median?
If a distribution is left-skewed, what is the typical relationship between mean and median?
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Mean $<$ median. Left tail pulls mean lower than median.
Mean $<$ median. Left tail pulls mean lower than median.
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If a distribution is right-skewed, what is the typical relationship between mean and median?
If a distribution is right-skewed, what is the typical relationship between mean and median?
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Mean $>$ median. Right tail pulls mean higher than median.
Mean $>$ median. Right tail pulls mean higher than median.
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What is the rule for identifying outliers using fences based on $Q_1$, $Q_3$, and $IQR$?
What is the rule for identifying outliers using fences based on $Q_1$, $Q_3$, and $IQR$?
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Outliers: $x<Q_1-1.5IQR$ or $x>Q_3+1.5IQR$. Values beyond $1.5$ times $IQR$ from quartiles are outliers.
Outliers: $x<Q_1-1.5IQR$ or $x>Q_3+1.5IQR$. Values beyond $1.5$ times $IQR$ from quartiles are outliers.
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Two boxplots have equal medians, but Plot A has larger $IQR$ than Plot B; which has greater spread?
Two boxplots have equal medians, but Plot A has larger $IQR$ than Plot B; which has greater spread?
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Plot A has greater spread. Larger $IQR$ means more variability in data.
Plot A has greater spread. Larger $IQR$ means more variability in data.
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What does the shape of a distribution describe (for example, symmetric, skewed, unimodal)?
What does the shape of a distribution describe (for example, symmetric, skewed, unimodal)?
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Overall pattern: symmetry/skewness, modality, and tail behavior. Shape reveals how data clusters and extends from center.
Overall pattern: symmetry/skewness, modality, and tail behavior. Shape reveals how data clusters and extends from center.
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What is the center of a distribution, and which two statistics are most common for center?
What is the center of a distribution, and which two statistics are most common for center?
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Typical value; most common are mean and median. Center represents where most data values cluster.
Typical value; most common are mean and median. Center represents where most data values cluster.
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What does the spread of a distribution describe, and which two statistics are most common for spread?
What does the spread of a distribution describe, and which two statistics are most common for spread?
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Variability; most common are $IQR$ and standard deviation. Spread measures how far data extends from center.
Variability; most common are $IQR$ and standard deviation. Spread measures how far data extends from center.
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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. Median uses middle value, unaffected by extreme values.
Median. Median uses middle value, unaffected by extreme values.
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What is the center of a distribution, and which two statistics commonly represent it?
What is the center of a distribution, and which two statistics commonly represent it?
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Typical value; mean and median represent center. Center shows where most data clusters.
Typical value; mean and median represent center. Center shows where most data clusters.
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Which data set has the larger center if $\text{median}_A=52$ and $\text{median}_B=47$?
Which data set has the larger center if $\text{median}_A=52$ and $\text{median}_B=47$?
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Data set $A$. $52>47$, so $A$ has higher typical value.
Data set $A$. $52>47$, so $A$ has higher typical value.
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Find the outlier cutoffs if $Q_1=10$ and $Q_3=18$ using the $1.5\times\text{IQR}$ rule.
Find the outlier cutoffs if $Q_1=10$ and $Q_3=18$ using the $1.5\times\text{IQR}$ rule.
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Lower $=-2$, upper $=30$. $\text{IQR}=8$, so bounds are $10-12=-2$ and $18+12=30$.
Lower $=-2$, upper $=30$. $\text{IQR}=8$, so bounds are $10-12=-2$ and $18+12=30$.
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Which data set has the larger spread if $\text{IQR}_A=12$ and $\text{IQR}_B=8$?
Which data set has the larger spread if $\text{IQR}_A=12$ and $\text{IQR}_B=8$?
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Data set $A$. $12>8$, so $A$ has more variability.
Data set $A$. $12>8$, so $A$ has more variability.
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A data set gains one extreme high value. Which statistic changes more: mean or median?
A data set gains one extreme high value. Which statistic changes more: mean or median?
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Mean changes more. Mean includes all values; median only uses middle.
Mean changes more. Mean includes all values; median only uses middle.
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A data set gains one extreme high value. Which statistic changes more: standard deviation or IQR?
A data set gains one extreme high value. Which statistic changes more: standard deviation or IQR?
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Standard deviation changes more. SD uses all values; IQR only uses quartiles.
Standard deviation changes more. SD uses all values; IQR only uses quartiles.
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What does the shape of a distribution describe (in words) when comparing data sets?
What does the shape of a distribution describe (in words) when comparing data sets?
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Symmetry or skewness and the number of peaks (modality). Shape includes distribution pattern and peak count.
Symmetry or skewness and the number of peaks (modality). Shape includes distribution pattern and peak count.
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What does the spread of a distribution describe, and name two common measures?
What does the spread of a distribution describe, and name two common measures?
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Variability; IQR and standard deviation measure spread. Spread shows how dispersed the data is.
Variability; IQR and standard deviation measure spread. Spread shows how dispersed the data is.
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Which measure of spread is more resistant to outliers: IQR or standard deviation?
Which measure of spread is more resistant to outliers: IQR or standard deviation?
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IQR. IQR uses middle 50%, unaffected by extremes.
IQR. IQR uses middle 50%, unaffected by extremes.
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What is the $1.5\times\text{IQR}$ rule for identifying outliers using quartiles?
What is the $1.5\times\text{IQR}$ rule for identifying outliers using quartiles?
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Outliers are $<Q_1-1.5\text{IQR}$ or $>Q_3+1.5\text{IQR}$. Values beyond these bounds are unusually extreme.
Outliers are $<Q_1-1.5\text{IQR}$ or $>Q_3+1.5\text{IQR}$. Values beyond these bounds are unusually extreme.
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