6.0 Наppiness starts to increase at 5.5 age 46 Наpiness peaks at age 74 5.0 4.5 15 60 20 30 40 45 46 50 70 74 80 Age (years) Happiness scale (1 to 7)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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?
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