The heights of women in the US approximately follow a bell shaped curve. What do you think that means?
It means that heights (h) are distributed according to a formula
N(h) = exp-[(h-m)/a)]^2 , where
m is the most probable (and average) height
a is the standard deviation, sometimes called sigma
If you plot N vs. h, it looks like an upside-down bell.
The bell-shaped curve, also known as the normal distribution or Gaussian distribution, is a statistical concept that describes the frequency distribution of a dataset. When applied to the heights of women in the US, a bell-shaped curve indicates that most women tend to have heights close to the average, with fewer women at the extremes.
In simpler terms, a bell-shaped curve means that there are more women who are of average height, and as height deviates from the average, the number of women gradually decreases. So, there are fewer women who are significantly shorter or taller compared to the majority.
To obtain the bell-shaped curve for the heights of women in the US, statisticians collect a large sample of women's heights and plot them on a graph. The graph is then analyzed to determine if the data conforms to a bell-shaped distribution. If it does, it indicates that the variable being measured (in this case, height) is likely normally distributed in the population.