What’s Wrong? Heights of adult males are known to have a normal distribution, as described in this section. A researcher claims to have randomly selected adult males and measured their heights with the resulting relative frequency distribution as shown here. Identify two major flaws with these results.

Heights (cm)	Relative Frequency
130-144	23%
145-159	25%
160-174	22%
175-189	27%
190-204	28%

The relative frequency distribution of the heights of males (in cm) is given.

The heights of the men are considered to follow a normal distribution.

A frequency distribution is considered to follow the normal distribution if the frequencies gradually increase from a small value, achieve a maximum value, and then gradually decline.

Here, the relative frequencies of all the classes are approximately equal to each other.

There is no pattern of an eventual increase in the frequencies followed by a gradual decline.

Thus, the heights of the men as per the given distribution do not appear to be normally distributed. This is one flaw with the given frequency distribution.

It is known that the sum of the relative frequencies for all classes should be equal to 100%.

Here, the sum of the frequencies is computed below.

$$\begin{gathered} \text{Sum}\text{of}\text{all}\text{relative}\text{frequencies}=23\%+25\%+22\%+27\%+28\% \\ =125\% \end{gathered}$$

As the sum of all relative frequencies exceeds 100%, there is a major flaw in the given frequency distribution.