Question

Let's say you have collected data from a large sample of participants on some variable that you think is normally distributed. In this case use IQ scores. Describe the variable and state whether the scale of measurement is nominal, ordinal, interval, or ratio, and why you came to that conclusion. What does it mean to say the variable is normally distributed? What is probability value and explain how a probability value of .05 in your example is related to the normal curve.

Answer 1

When we collect dataset form a population that is normally distributed then it has a bell shaped density function .

Suppose here in the above example it is given that IQ scores are collected then the variable IQ score is normally distributed as IQ score is in numbers and we can quantify that number So the data is of interval type because here IQ scores will lies between certain 2 numbers .

Normal probability curve looks like :

IQ scores are normally distributed in the sense that we know that most of the people have an average IQ scores .

a very few of them have very less number of IQ scores and a very few of them will have IQ scores very high which the above graph shows that it is very low at tails and peak at mean where most of them have average IQ .

Here suggests us that we usually takes this 0.05 because if a population is normally distributed then almost 95 % of population is expected to lies in limits .