Mean vs Median
In right-skewed data, which is larger?
mean
Same mean, different spread → what differs?
standard deviation
A Sample differs from a population because of…
Sampling variation
Which rule uses mean?
2σ rule
Best summary for skewed income data
Median
In left-skewed data, which is smaller?
mean
Same median, different IQR → what differs?
Variation
Larger samples are generally…
More accurate or representative of the population
Which rule uses quartiles?
IQR rule
If most values are clustered tightly, the data is…
Consistent and reliable
Why mean is not ideal for skewed data?
Sensitive to extreme values
What does a consistent distribution look like?
smaller spread / smaller IQR
A subset of the population
Sample
In skewed data, which rule is better?
IQR rule
A dataset has no outliers by the IQR rule but has extreme values. What does this suggest about the distribution?
likely skewed; extreme values are part of the distribution
Can mean = median in skewed data?
no (generally not)
Two datasets overlap heavily—what does this mean?
They are similar distributions. Similar values
Why might a sample of 50 fans give different shirt size proportions than the whole school?
random variation / not perfectly representative
Can a value be outlier by one rule but not the other?
yes
A long tail indicates…
skew
A distribution has mean > median and a long right tail. Explain how the extreme values are affecting the mean.
High values pull the mean to the right (larger than the median)
Why compare medians instead of means for skewed data?
The median is resistant to extreme values
Best way to improve prediction...
larger/more representative sample
Why 2σ rule may flag more outliers in skewed data
mean/SD affected by skew
A dataset is right-skewed. Explain why the mean is not a good representation of a “typical” value in context.
mean is pulled by high values; median better represents typical values