Statistics: Misleading Statistics and Graphs
Spotting bias, distorted scales, and unfair comparisons
Statistics: Misleading Statistics and Graphs
Spotting bias, distorted scales, and unfair comparisons
Statistics - Grade 6-8
- 1
A bar graph compares two test scores: Class A scored 84 and Class B scored 88. The y-axis starts at 80 instead of 0, making Class B's bar look much taller. Explain why this graph is misleading.
Check where the y-axis begins before comparing bar heights.
The graph is misleading because starting the y-axis at 80 exaggerates the difference between 84 and 88. The actual difference is only 4 points, so the bars should not look extremely different. - 2
A line graph shows the price of a school lunch over four years: $2.50, $2.75, $3.00, and $3.25. The graph uses equal spacing on the x-axis, but the years shown are 2019, 2020, 2023, and 2024. What is misleading about this graph?
Look at whether the years are evenly spaced in time.
The graph is misleading because the time intervals are not equal. The gap from 2020 to 2023 is three years, but it is shown with the same spacing as one-year gaps. - 3
A survey says, "80% of students love the new cafeteria menu." The survey was taken from only 10 students sitting near the pizza line. Explain why this statistic may be unreliable.
Think about sample size and whether the group represents the whole school.
This statistic may be unreliable because the sample is very small and not representative of all students. Students near the pizza line may have different opinions from the rest of the school. - 4
A pictograph shows bike sales. One bike picture represents 10 bikes, but in the final row the store uses a bike picture twice as tall and twice as wide to show 20 bikes. Why can this be misleading?
When both height and width change, the picture's area changes a lot.
This can be misleading because making the picture twice as tall and twice as wide makes it look four times as large by area. Viewers may think sales increased more than they really did. - 5
A pie chart shows favorite sports: soccer 40%, basketball 35%, baseball 30%, and swimming 20%. Explain the problem with this graph.
The graph has a problem because the percentages add to 125%, but a pie chart should total 100%. The data cannot all be parts of one whole as shown. - 6
A store ad says, "Sales doubled this week." Last week the store sold 2 skateboards, and this week it sold 4 skateboards. Explain how the claim could be technically true but still misleading.
Compare the percent change with the actual number of items.
The claim is technically true because 4 is double 2. It can still be misleading because the total number of skateboards sold is very small, so the increase may not be as impressive as it sounds. - 7
The mean price of five backpacks is $28. The prices are $20, $22, $24, $26, and $48. Why might the mean be misleading for describing a typical backpack price?
The mean may be misleading because the $48 backpack is much more expensive than the others and raises the average. The median, $24, may better describe a typical price in this set. - 8
A company claims its cereal is "the top choice of families" because 52 out of 100 families in its survey chose it over one other cereal. What important information is missing?
Look for details about the survey and the comparison group.
Important missing information includes how the families were chosen, what the other cereal was, and whether more cereal brands were compared. Without this information, the claim may be biased or incomplete. - 9
A graph compares library visits in May and June. May had 400 visits and June had 500 visits. The title says, "Library Visits Explode by 100%!" Explain why the title is misleading.
The title is misleading because visits increased from 400 to 500, which is an increase of 100 visits. That is a 25% increase, not a 100% increase. - 10
A line graph shows ice cream sales and sunburn cases both rising during the summer. A student says, "Ice cream causes sunburns." Explain the mistake in this conclusion.
Two things can happen together without one causing the other.
The mistake is confusing correlation with causation. Ice cream sales and sunburn cases may both rise because of hot, sunny weather, not because ice cream causes sunburns. - 11
A bar graph compares the number of books read by three classes, but the y-axis has no numbers or scale. Why is the graph hard to trust?
The graph is hard to trust because there is no scale to show the actual values. Without numbers on the y-axis, the viewer cannot tell how large the differences really are. - 12
A 3D bar graph shows two sales numbers: Store A sold 90 items and Store B sold 100 items. The 3D effect makes Store B's bar look much larger because it appears wider and deeper. Explain why a simple 2D bar graph would be better.
Extra decoration can make differences look larger than the data show.
A simple 2D bar graph would be better because it shows differences using height without extra visual effects. The 3D width and depth can exaggerate the difference between 90 and 100. - 13
A school reports, "Most students improved in math." The report only includes students who attended after-school tutoring and leaves out all other students. Why might this be misleading?
Check who was included and who was left out.
This might be misleading because the report does not include all students. Students who attended tutoring may not represent the entire school, so the conclusion may not apply to everyone. - 14
A website says, "9 out of 10 dentists recommend this toothpaste." It does not say how many dentists were asked or how they were selected. What should you question about this statistic?
You should question the sample size and how the dentists were selected. If only 10 dentists were asked or if the sample was biased, the statistic may not be reliable. - 15
A graph shows a phone battery dropping from 100% to 95% in one hour, but the y-axis only shows 94% to 100%. The line looks very steep. Explain how to make the graph less misleading.
A zoomed-in scale can make a small change look dramatic.
The graph would be less misleading if the y-axis showed a wider range, such as 0% to 100%, or if the graph clearly warned that the scale is zoomed in. This would help viewers see that the battery only dropped 5 percentage points.