MEAN OR MEDIAN
Which measure is better when data are skewed?
Median
Identify the outlier:
3, 4, 5, 6, 25
Outlier = 25
A survey of 40 seniors describes all students.
What is the sample?
Sample = 40 seniors.
Favorite lunch option
Nominal, Ordinal, Interval, or Ratio?
Nominal (categories, no order)
Data: 4, 5, 6, 7, 40
Which measure better represents the data?
Median (6)
Reason: 40 is an outlier pulling mean up.
How does an outlier affect the mean?
Outliers pull the mean toward them.
What is the population in this study?
“We surveyed 50 students to understand study habits.”
Population = all students.
Temperature in °F
Nominal, Ordinal, Interval, or Ratio?
Interval (equal intervals, no true zero)
Why might the mean be misleading in income data?
Mean is misleading in income data because extreme high incomes raise the average.
Which measure is resistant to outliers?
Median is resistant.
Is this a statistic or a parameter?
“The average GPA of 60 surveyed students was 3.1.”
Statistic (because 60 surveyed students = sample).
Class ranking (1st, 2nd, 3rd)
Nominal, Ordinal, Interval, or Ratio?
Ordinal (ranked, but differences not equal)
Two classes have the same mean.
Class A range = 4
Class B range = 20
Which class is more consistent? Why?
Class A (range 4) is more consistent.
Smaller range = less variability.
Dataset A and B have same median.
A has an extreme high value.
Which measure will differ more: mean or median? Why?
The mean will differ more because it is sensitive to extreme values.
Why can we not generalize a sample to an entire state without caution?
Small sample may not represent entire state; possible bias.
Hours of sleep per night
Nominal, Ordinal, Interval, or Ratio?
Explain why.
Ratio (true zero, meaningful ratios)