 Normal Distribution and z Scores Explained - Introductory Statistics

The properties of the normal distribution are explained in the video, including how the normal distribution is symmetrical, how mean = 0 and standard deviation = 1, how the mean, median, and mode are equal, positive and negative z scores, and what a z score means.
Video Transcript:
In this video we'll take a look at the z-score normal distribution including some of the properties of the z-score normal distribution. And first of all the z score distribution is symmetrical. And what that means is if we define the area under this curve as one hundred percent or 1.00 if we're speaking in terms of proportions, that means that all of the values are underneath this curve or within this curve. One hundred percent of the values fall within this curve. Now the fact is symmetrical means that if we drew a line down the center of this distribution where it ends in 0 which is equal to the mean of the z score distribution a mean of zero then 50% or .50 of the values occur to the left of the mean and 50% or .50 the values occur to the right of the mean. So in other words that line splits the distribution exactly in half because it's symmetrical. Next we can see that the mean of a z-score distribution is equal to 0 which I just said a minute ago. So the mean is equal to 0 and the standard deviation is equal to one. Now here on your screen we're using the population symbols the Greek symbols for the mean this is called Mu is equal to 0 and sigma or the standard deviation is equal to one. And then finally the mean the median and the mode are all equal in a z-score distribution so if we know that the mean is equal to 0 then that tells us also that the median and the mode are also equal to 0. Now this occurs in a z-score normal distribution but it's necessary that the distribution is normal in order for the properties of the fifty percent on each side to be true we could calculate these scores on any distribution but it's required that the distribution be normal in order for these properties to hold here all of them and then for us to look at proportions in the back of our introductory statistics textbook to pull out proportions for various z-score values which we'll talk about in other videos. One last thing before we close here, what is a z-score? Well a z-score tells you how far away a value is in terms of standard deviations from the mean. Let me show you what I mean there. So if we have a z-score of 1 the value that occurs right here that indicates it's one standard deviation above the mean and it's above the mean because it's positive. So a z-score of -2 as another example is two standard deviations below the mean and it's below because it's negative. A z score of zero means that the value is zero standard deviations away from the mean or no standard deviations away from the mean so if you think about that if it's zero standard deviations away that actually means that it's equal to the mean. So a z score of 0 is just equal to the mean. OK that's about it for the properties of the z-score normal distribution. Thanks for watching.
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Channel Description: For step by step help with statistics, with a focus on SPSS. Both descriptive and inferential statistics covered. For descriptive statistics, topics covered include: mean, median, and mode in spss, standard deviation and variance in spss, bar charts in spss, histograms in spss, bivariate scatterplots in spss, stem and leaf plots in spss, frequency distribution tables in spss, creating labels in spss, sorting variables in spss, inserting variables in spss, inserting rows in spss, and modifying default options in spss. For inferential statistics, topics covered include: t tests in spss, anova in spss, correlation in spss, regression in spss, chi square in spss, and MANOVA in spss. New videos regularly posted. Videos series coming soon include: multiple regression in spss, factor analysis in spss, nonparametric tests in spss, multiple comparisons in spss, linear contrasts in spss, and many more. Subscribe today!
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normal distribution
normal distribution curve
z score
bell shaped curve
standard score

2014年07月15日

添加到: Ajay Kamath 4 个月 前
excellent !!! Rob S 8 个月 前
Quick, informative and very simple - solved my problem. Thanks! NAVEEN KUMAR SINGH 9 个月 前
Sir can you send me the solution of 2016 to 2018 CIE 9709 S1 PAST PAPERS Karla Caceres 9 个月 前
I loved it!
NAVEEN KUMAR SINGH 9 个月 前
Karla Caceres hey are you good in S1 papers CIE Karla Caceres 9 个月 前
Thanks very simple!!!! Selfspot 2 年 前
Came for an answer and found it. Thanks! I put the link of this video in the summary I made and send it to some of my friends. Marco Oliveri 3 年 前
Great video! Concepts are explained very clearly, thank you.
+Marco Oliveri Thanks, Marco! Please let others know who might benefit from these as well!