Misleading Statistics: Homework

Check the scale, look for the outlier, and ask who was counted.

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Part A — Where Does the Scale Start? / 4

A bar rises above the starting line of the axis. Compare how tall the bars look with how different the numbers really are.

1.
An axis starts at 90, and two bars show 92 and 98. How tall does each bar rise above the start? Find how many times taller the second looks than the first.Answer
2.
An axis starts at 40, and bars show 45 and 55. How many times taller does the second bar look?Answer
3.
The same two bars, 92 and 98, are drawn from zero. How many times as large is the second as the first? Round to the nearest hundredth.Answer
4.
Where should a bar graph's scale start to be fair?Answer

Find the mean and the median. The mean is pulled toward an outlier, and the median isn't.

1.
Find the mean: 12, 14, 15, 13, 96Answer
2.
Find the median: 12, 14, 15, 13, 96Answer
3.
Pay in thousands: 31, 33, 35, 35, 36, 220. Find the mean and the median.MeanMedian
4.
For the pay above, which number is the fairer picture of a typical worker, the mean or the median?Answer
5.
Take the 220 out. What is the mean of the other five pay amounts?Answer

Type yes or no, then explain in your head why.

1.
A shoe store asks only the people leaving its own store whether they like shoes. Is the answer a fair picture of the whole town? Type yes or no.Answer
2.
Eight kids at a chess club all say chess is their favorite game. Does that show that most kids love chess? Type yes or no.Answer
3.
A poll says 8 out of 10 people like a movie. What three things would you want to know before you believe it?Answer

The coin values and the sides of the polygons are real.

1.
The values of six United States coins, in cents: penny 1, nickel 5, dime 10, quarter 25, half dollar 50, dollar coin 100.
a. Find the mean value. Round to the nearest hundredth.Answer
b. Find the median value.Answer
c. How many of the six coins are worth less than the mean?Answer
d. Which fits a typical coin better, the mean or the median?Answer
2.
The number of sides of eight polygons: triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, decagon 10, icosagon 20.
a. Find the mean. Round to the nearest hundredth.Answer
b. Find the median.Answer
c. Which value is the outlier?Answer

Write your answer in a sentence or two.

1.
Write five numbers whose mean is much bigger than their median. Say which number does it.Answer
2.
Find a graph or an ad and say how it could mislead. Which of the three questions catches it?Answer

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Total / 21

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Notes

Part A — the answers.

4
3
1.07
At zero. Your eye compares the sizes of the bars, so a scale that starts higher stretches small differences.

Part B — the answers.

Part C — the answers.

No. They had all just shopped for shoes.
No. The kids at a chess club are not a mix of all kids.
Answers vary. Good answers ask who was asked, how many people were asked, and how they were picked.

Part D — the answers.

a. 31.83 b. 17.5 c. 4 (the penny, nickel, dime and quarter). d. The median, because the dollar coin pulls the mean up.
a. 7.88 b. 6.5 c. 20, the icosagon.

Part E — one correct answer, and what a good explanation says.

Answers vary. One that works is 3, 4, 5, 6, 82: the median is 5, the mean is 100 ÷ 5 = 20, and the 82 does it.
Answers vary. A good answer names the trick, such as a scale that starts above zero, one huge value in an average, or a poll of only some people.