Let's say you have collected data from a large sample of participants on some variable that you think is normally distributed. 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.

Normal Distribution

Statistics deals with collection and analyses of data from numerous sources. The variables analyzed may display varying distribution depending on the nature of the population. However, there exists the central limit theorem (CLT). CLT argues that given the sample size is considerably large, the distribution may follow a normal distribution. Consequently, the study studies a normal random variable. After that, it details the measurement scale and the concept of probability values.

Variable Description

The study investigated the height of 100 grade K12 students. The researcher used the tape measure to ascertain their height. He discovered that the variable is a dependent variable. The reason being, the age, race, and the upbringing could affect the height of the respondents. Moreover, the study noted that the variable was a ratio scale (Stephanie, 2014). The argument is, the respondent who has zero height means does not have any length.

There are multiple characteristics of the heights that illustrated that they follow a normal distribution. For instance, the students’ heights are more near the means as opposed to the extremes (Frost, n.d). Moreover, the numbers of students whose heights are lower than the means are almost equal to those whose heights exceed the average. The alteration of the mean also shifts the shape from the previous position (Frost, n.d). It is also evident that increasing the standard deviation increases the flatness of the curve.