maths - frequency polygon

hi has anyone got any ideas or where i can start with this
“without using any data or putting scales on your axes sketch a frequency polygon that you would expect for a very large sample of the following data:
a) height of people in the uk today
b) average daily wind speed on heathrow
c) iq of people in a country

Reply 1

MouldyVinegar

For a) what would you say about the heights of most people? For example, roughly what percentage of people do you think are between 5ft3 and 6ft2? What about the percentage of people between 6ft3 and 7ft2, and the percentage between 4ft3 and 5ft2? Do you think there are more people in the range 5ft3-6ft2 than there are people outside of this range, even though they can be many more different heights? You should notice that most people tend to be around the same height, with very few people being very tall and very few being very short. That is, it would follow a bell-shaped (or normal) distribution. Similarly, would you expect most people to have average intelligence, with only a few people having very high IQs and very few having very low IQs?
For b), that is somewhat more difficult, simply because wind speeds are far less intuitive. I would wager is also normally distributed, because each wind speed is random, and you would expect wind speeds to be near the average, and having no wind or hurricane strength winds to be very rare. However, it may also be better modeled as say a Poisson distribution, but they probably wouldn't expect you to know the specifics of it, and a Poisson and Normal distribution are both rather close (if you squint hard enough anyways)