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Hello my name is Beth Dixon and this is the second video in a series based on Vicki Borlaug's PowerPoint presentation
oops I cannot get the screen to fast forward.. but a PowerPoint presentation based on z-scores comparing values on different scales
I wish to thank Mrs. Borlaug for allowing me to use her PowerPoint presentation in making this set of videos
we are on to topic two and I will start this video on the second topic comparing values on different scales
instead of explaining exactly what I mean I will just go straight to the example and I think the
example will do a better job at explaining than any words I could use here
there are two or mechanical aptitude test available
one test is called Engines-A-New and has mean of 436 and a standard deviation of 14
the other test called Fix-It has a mean a 62 and a standard deviation of four
Tom takes Engines-A-New test and makes a 411 Sara takes the Fix-It test and gets a 57
Who has the higher relatives score
justify
so this is a typical problem that our faculty ask on our tests asking students to compare two values in this case
two aptitude test scores that use different scales
just because the Engines-A-New test has the score of
of 411 and Sara's
Fix-It test gets a 57 doesn't mean that the Engines-A-New test or Tom
has the better score
we need to standardize the scores in order to compare the two scores another way to say this is we need to figure out how many
standard deviations each score is above or below each mean in other words we need to find each z-score
as we do the problem
we want to look at each test separately
organizing our data so our numbers do not get confused
first Engines-A-New Test
look for the mean
which is 436
look for the standard deviation
which is 14
look for Tom's score on this test or look for who takes this test in this case it's Tom and Tom gets a 411
and we've organized that information
altogether
and we have for the Engines-A-New a mean of 436 a standard deviation of 14 and that Tom gets a 411
next list organize our information for the Fix-It test it has a mean of 62
a standard deviation
of four
and Sara took this test
and got a 57
notice the organization again you do want to be able to keep up with your information
you cannot compare the test scores because they are on different scales we have can
however compared z-values because the z- values are the number of standard deviations
above and below the mean let me say that again
why can we compare the z-scores because
z-scores measure this same thing the number of standard deviations above or below the mean
so let's go back
and look at Tom's Engines-A-New test so let's find the number of standard deviations from the mean that Tom score is
find the number of standard deviations from the main by using the formula z equals x
minus the mean divided by the standard deviation x minus mu over sigma
x=411 minus 436 which is the mean divided by 14 which is the standard deviation
411 minus
436
gives me ....................
I've think ...let me reach for my calculator here because I did not do that part
by itself 411-436 gives me -25 divided by 14
rounded to 2 decimal places again z-scores should always be rounded to 2 decimal places gives me a -1.79
Be sure that you do the top
of your of formula then divide by the bottom or put place the top of your calculation in
parentheses divided by the bottom otherwise you will not get the correct answer
so Tom's score is a -1.79 so because it is negative remember that means he's scored the left of the mean he scored below the mean
OK let's look at Sara's test she got a 57
so we want to find the number of standard deviations from the mean again using the formula
57 for her score minus the mean of 62 divided by the number of standard deviations 57 -62
gives me -5 and negative five divided by four gives me -1.25 again it is below the mean and so we have their two
z-scores now that we know how many standard deviations each
scored
we can compare
make our of comparisons because we can compare z-scores Who has the higher relative score
were looking for who scored relatively higher on their test
now we need to be careful with our negative numbers and to illustrate this
I will show you the number line here is our z- score number line and let's place both Tom and Sara on the number line
so the scores to the right are higher who has the higher relative score
Sara has the higher relative score because her score is to the right of Tom's
here are some exercises for you to try pause if you wish to do these
thank you for watching and as always, please feel free to stop by and see me in MBSS 222 here Walters State
an again thanks to Mrs. Borlaug for allowing us
to use
her videos