5 x 12 ÷ [-12 + {15+ (4 - 13)}] please solve this clearly
2 answers:
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Answer:
a.
∑x=109, ∑x²=4173, ∑y=87, ∑y²=2083.
b.
sample mean for x=10.9.
variance for x=331.66.
standard deviation for x=18.21.
sample mean for y=8.7.
variance for y=147.34.
standard deviation for y=12.14.
c.
75% Chebyshev interval around the mean for x values
-25.52,47.32
75% Chebyshev interval around the mean for y values
-15.58,32.98
The interval shows that Vanguard Balanced index has smaller spread.
d.
coefficient of variation for x=167.06%
coefficient of variation for y=139.54%
Smaller CV means lower risk so, smaller CV is better.
Step-by-step explanation:
Note: ALL ANSWERS ARE ROUNDED TO TWO DECIMAL PLACES
a.
∑x=17+0+17+28+28+27+29−12−12−13=109,
∑x²=17²+0²+17²+28²+28²+27²+29²+(−12)²+(−12)²+(−13)²=4173,
∑y=14−2+27+18+20+11+14−2−3−10=87,
∑y²=14²+(−2)²+(27)²+(18)²+(20)²+(11)²+(14)²(−2)²+(−3)²+(−10)²=2083.
b.
sample mean for x=∑x/n=109/10=10.9.
x-mean
6.10
-10.90
6.10
17.10
17.10
16.10
18.10
-22.90
-22.90
-23.90
sum(x-mean)²=6.10 ²+(-10.90 )²+6.10 ²+17.10² +17.10²+ 16.10² +18.10² +(-22.90 )²+(-22.90 )²+(-23.90 )²=2984.9
Variance for x=331.66.
standard deviation for x=√variance for x
standard deviation for x=√331.66
standard deviation for x=18.21.
sample mean for y=∑y/n=87/10=8.7.
y-mean
5.30
-10.70
18.30
9.30
11.30
2.30
5.30
-10.70
-11.70
-18.70
sum(y-mean)²=5.30 ²+(-10.70 )²+18.30² +9.30² +11.30² +2.30² +5.30² +(-10.70 )²+(-11.70 )²+(-18.70 )²=1326.1
variance for y=147.34.
standard deviation for y=√variance for y
standard deviation for y=√147.34
standard deviation for y=12.14.
c.
75% Chebyshev Interval
mean±k standard deviation
We have to find value of k.
k²=4
k=2
so, 75% Chebyshev Interval for x
10.9±2*(18.21)
[-25.52,47.32]
75% Chebyshev Interval for y
8.7±2*(12.14)
[-15.58,32.98]
The interval shows that Vanguard Balanced index has smaller spread.
d.
CV for x=167.06%
CV for y
Cv for y=139.54%
The smaller CV shows the smaller amount of risk so, smaller CV is better.