Chapter 2: Q. 2.169 (page 86)

Happiest Age. An article, titled "We're Happiest at 74; It's All Downhill till 40, Then Life Gets Better, Say Scientists," included a graph, similar to the following one, of a happiness scale versus age. The article argues that happiness decreases until the age of 46 and then increases again and that people are happiest when they hit 74. Notice the horizontal axis as well as the vertical axis. [SOURCE: Graph from Daily Mail. Copyright 2010 by Associated Newspapers Ltd. Used by permission of Associated Newspapers Ltd.]
a. Cover the numbers on the vertical axis of the graph with a piece of paper.
b. What impression does the graph convey regarding the percentage drop in happiness between the ages of 15 and 20?
c. Now remove the piece of paper from the graph. Use the vertical scale to find the actual percentage drop in happiness between the ages of 15 and 20.
d. Why is the graph potentially misleading?
e. What can be done to make the graph less potentially misleading?

Short Answer

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Ans:

(a) First we cover the numbers on the vertical axis of the graph with a piece of paper.

(b) The given graph represents happiness compared to years. If the vertical axis of the graph is covered, the graph shows that happiness decreases by $25 %$ when the age is between $15 a n d 20 y e a r s$ .

(c) When the paper is removed from the vertical axis, the actual drop from $5.5 t o 5.25 b e t w e e n 15 a n d 20 y e a r s$ . That is, the actual decrease is $4.5 % (= \frac{0.25}{5.5})$ happiness.

(d) Without a precise scale, it would be like the happiness dropped to $50 %$ when the real decline was around $20 %$ . Moreover, a high value of $74$ indicates that there is a significant difference when a specific scale can be used. Also, on a horizontal scale, the time between events is misleading as the years can be equally divided.

(e) Possible changes to the graph to be more misleading than the vertical axis can be from $0 t o 6.5$ . Also, the horizontal scale can be divided equally.

Step by step solution

Step 1. Given information.

given,

An article, titled "We're Happiest at 74; It's All Downhill till 40, Then Life Gets Better, Say Scientists," included a graph, similar to the following one, of a happiness scale versus age. The article argues that happiness decreases until the age of 46 and then increases again and that people are happiest when they hit 74.

Step 2. (a) According to question.

First, we cover the numbers on the vertical axis of the graph with a piece of paper.

Step 3. (b) Description,

The given graph represents happiness compared to years. If the vertical axis of the graph is covered, the graph shows that happiness decreases by $25 %$ when the age is between $15 a n d 20 y e a r s$ .

Step 4. (c) Description,

When the paper is removed from the vertical axis, the actual drop from $5.5 t o 5.25 b e t w e e n 15 a n d 20 y e a r s$ . That is, the actual decrease is $4.5 % (= \frac{0.25}{5.5})$ happiness.

Step 5. (d) Description,

Without a precise scale, it would be like the happiness dropped to $50 %$ when the real decline was around $20 %$ . Moreover, a high value of $74$ indicates that there is a significant difference when a specific scale can be used. Also, on a horizontal scale, the time between events is misleading as the years can be equally divided.

Step 6. (e) Description,

Possible changes to the graph to be more misleading than the vertical axis can be from $0 t o 6.5$ . Also, the horizontal scale can be divided equally.