Normal Distribution and z Scores Explained – Introductory Statistics


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.

7 thoughts on “Normal Distribution and z Scores Explained – Introductory Statistics

  • October 17, 2015 at 2:45 pm
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    Great video!
    Concepts are explained very clearly, thank you.

    Reply
  • January 25, 2017 at 8:09 am
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    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.

    Reply
  • August 30, 2018 at 2:35 am
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    Thanks very simple!!!!

    Reply
  • August 30, 2018 at 2:35 am
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    I loved it!

    Reply
  • September 13, 2018 at 3:09 pm
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    Reply
  • October 3, 2018 at 9:10 am
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    Quick, informative and very simple – solved my problem. Thanks!

    Reply
  • February 15, 2019 at 11:11 am
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    excellent !!!

    Reply

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