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