Question

In: Math

Do calculation by hand and in the statistical program of choice.                         Given this dataset: 3,6,2,1,2,3,4 Convert...

Do calculation by hand and in the statistical program of choice.                 

       Given this dataset: 3,6,2,1,2,3,4

  1. Convert each of these values to a z-score.
  2. What percentage of cases would you expect to fall below 2?
  3. What score would be at the 90th percentile?

Solutions

Expert Solution

Sol:

For the given sample

mean=sum/total=21/7=3

std dev=1.632993

Z score=x-mean/sd

for X=3

z=3-3/1.632993=0

for x=6

z=6-3/1.632993=1.837117

for x=2

z=2-3/1.632993

z=2-3/1.632993=-0.6123725

for x=1

z=1-3/1.632993=-1.224745

for x=2

z=2-3/1.632993=-0.6123725

for x=3

z=3-3/1.632993=0

for x=4

z=4-3/1.632993

z=0.6123724

  1. What percentage of cases would you expect to fall below 2?

z=x-mean/sd

=2-3/1.632993

z=-0.6123724

P(Z<--0.6123724)

=P(Z<-0.612)

==1-P(Z<0.612)

=1-0.7291

=0.2709

=0.2709*100

=27.09%
percentage of cases would you expect to fall below 2 is 27.09%

  1. What score would be at the 90th percentile?

z score for 90th percentile is

z=1.281552

z=x-mean/sd

1.281552=x-3/1.632993

x=1.281552*1.632993+3

x=5.092765

core would be at the 90th percentile is 5.09

Rcode:


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