Q.2.169 - Elementary Statistics

Question

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 (c) $2010$ by Associated Newspapers Lid. 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?

Step-by-Step Solution

Answer

(a) Disregard the vertical axis' scale (b). 

(b) There is a significant increase in happiness after the age of $50$.

(c) There is a modest rise in happiness after persons reach the age of $50$.

(d) The graph is misleading 

(e) Redesign the graph.

Part (a) Step 1: Given information

The given data is 

Part (a) Step 2: Explanation

For the time being, disregard the vertical axis' scale (b).

Part (b) Step 1: Given information

The given data is 

Part (b) Step 2: Explanation

After the age of $15$, there appears to be a significant reduction in happiness. People in their forties are generally content.

There is a significant increase in happiness after the age of $50$.

Part (c) Step 1: Given information

The given data is 

Part (c) Step 2: Explanation

After the age of $15$, there appears to be a minor drop in happiness. People in their forties are generally content.

There is a modest rise in happiness after persons reach the age of $50$.

Part (d) Step 1: Given information

The given data is 

Part (d) Step 2: Explanation

The graph is misleading because if you don't account for the vertical axis scaling, you can come to the wrong conclusion.

Part (e) Step 1: Given information

The given data is 

Part (e) Step 2: Explanation

We could redesign the graph with a vertical axis that starts at 0 to fix the misleading graph.