What is the difference between a normal distribution and a standard normal distribution?
The Standard Normal Distribution is a specific instance of the Normal Distribution that has a mean of ‘0’ and a standard deviation of ‘1’.The visual way to understand it would be the following image (taken from here):The four curves are Normal distributions, but only the red one is Standard Normal (since it’s mean is zero, which means that’s where it’s centred, and its standard deviation is one, which basically tells us “how much the bell opens” to put it colloquially).So, if one is just a specific instance of the other, what purpose does the distinction serve?Suppose you have a data set of scores which are normally distributed with a mean of 86 and a standard deviation of 14. You pick a random test without looking at the score and you want to know the probability the score was below… say 72.What you can do is take the probability density function;and calculate the probability P(X<72) integrating on this function from -∞ to 72, replacing your SD and mean on the function. But it is a tedious integration at best. Instead, if you standardise your function then you can get it much easier.To do this, you subtract the mean from the value you want to examine (in this case 72) and you divide by the SD. So:[math]P(X<72)=P(X<(72−86)/14)=P(X<−1) [/math]So now you know that P(X<72) on your own Normal Distribution is equivalent to P(X<-1) on the Standard Normal Distribution.You are now interested in the area of the region which is left to the -1 (which as you can see is .1587 or 15.87% probability that the score is lower than 72).To get this value you can integrate on the SND density function or (much preferably) you can search on the normal distribution table (or z-table) which resumes the results of many possible evaluations so you don’t have to integrate. In this case, you just look for the -1 on the left and the 00 on the top (because it is -1.00) and you can see that the probability is .1587.Hope it helped.
How is the process of forming a histogram similar to a frequency distribution for qualitative data?
Not a huge difference, although I’m a little unclear as to what you mean by a frequency distribution in qualitative research. Quantitative can use that too, especially if the variable is categorical or ordinal.All a histogram is is a bar graph, which can represent frequency, density, etc, of the sample across a metric. The process to create one is pretty much the same, especially if you’re doing this by hand— each bar represents a range (e.g. 1–10, 11–20, 21–30) and you simply count the frequency that fell into that range. In many (all?) cases, the bars are next to each other since it’s better at showing the distribution (e.g. normal distribution). Also, density is sometimes used, since proportion is a more standardized metric than frequency.A histogram— bars next to each other, usually since it forms a curve of some sort. This is a density graph, since it shows the percent of total, and it forms a roughly normal distribution.A frequency graph. Bars not necessarily next to each other, and not continuous (it’s ordinal). This appears uniform distribution (except F-5) and the metric is simply # of tornadoes, not % of total.
What is the relationship between frequency and probability (y-axis) in a normal distribution graph?
Normal Distribution or Gaussian Distribution is one of the significant continuous probability distribution.In the above figure of probability distribution function,Red line represents the standard normal distribution with mean=0 and variance=1. Most of the times, mathematicians and statisticians seems to use probability and frequency interchangeably in probabilistic analysis as they are closely related,but the actual difference is that the relative frequency of occurrence of an event, observed in a number of repetitions of the experiment, is a measure of the probability of that event.The frequentist interpretation is a philosophical approach to the definition and use of probabilities. In normal distribution graph defined for continuous probability distribution,frequency and probability plotted along y-axis are same,with continuous random variable(X) along x-axis.
How do you work out probability using a histogram?
Ok so I have a histogram with IQ scores on the X axis and frequency density on the Y axis and my task is to work out the probability that an individual's IQ score is greater than 115. So how would I go about working out the probability?
Histograms! Statistics coursework help!?
Ok, I know how to draw them and how to calculate values, its just that in my coursework i am loosing marks for not explaining things. So what do histograms exactly show about your data, like I'm talking about the spread or correlation. Things like that! Thank you!