Samples
A poll of citywide voting preferences is conducted by calling people between 10a.m. and 2p.m. on weekdays. What is the sampling problem?
Nonrepresentative sample (employed people are not available)
A store states the “average TV costs eight hundred dollars,” but a few high end models skew the result upward. What type of average is likely being used?
Mean.
Two neighborhoods have the same average temperature. One ranges from freezing to 110 degrees, the other stays between 60 and 70 degrees. What key concept is being ignored?
Dispersion (range, variance, standard deviation).
A bar chart begins at 98 instead of 0, making small differences look large. What is this manipulation called?
Chopping off the axis / nonzero baseline.
A cereal brand claims “30% less sugar” without stating the base. Why is the statement misleading?
Missing percentage base; 30% less than what?
A quality inspector checks every tenth item on a conveyor belt. The belt has a repeating flaw every nine items. What is the issue?
Systematic bias: selection process aligns with the defect pattern, violating randomness.
A neighborhood’s “average age is 30.” 90% of residents are over sixty. Which average must this be?
Mean; it hides the distribution.
A day care reports a mean age of 4. All children are aged 1, 7, or 8. What is the problem.
High variance; mean is not representative.
A pictogram shows a barrel twice as tall and twice as wide to represent “double production.” What illusion does this create?
Area/volume distortion
A company cuts salaries by 20%, then raises them by 20% the next year. Why is pay not restored?
Percentages use different bases; salary ends lower.
A nutrition company surveys only customers at a marathon expo. It claims, “80% of people prefer our protein bar.” What is the bias here?
Biased sample due to nonrandom selection and psychological factors (health conscious group).
A realtor says the “average home has 3 bedrooms.” Half have 2 bedrooms, half have 4. Why is this claim misleading?
Mean is three, but mode and median are not. No actual 3 bedroom homes exist.
A company uses mean salary to claim pay is “competitive” hiding that most workers make far below that figure. Which measure better reflects worker experience?
Median or mode; dispersion shows inequality.
A profit curve is shown without labeled axes. Why is the graph meaningless?
No scale, so no information about magnitude or timeframe.
A charity says a campaign is “80% successful” because they raised 16 million of a 20 million dollar goal. The real goal was to raise 5 million (from fifteen to twenty). What is the true success percentage?
Twenty percent; only one million of the five million goal was raised.