Question

Compute the weighted average (round to the nearest cent) for the following table of values:

x	f(x)
$ 5	25
$ 20	11
$ 30	8
$ 75	3
$ 100	1

Also, what is the median dollar value from this data?

Compute the geometric mean return (rounded to 4 decimal places) for the following:

Year	Return
1	15%
2	-20%
3	30%
4	-8%
5	25%

If you invested $1,200, how much would it be worth after 5 years (round to the nearest cent)?

When you answer the question put the 4 answers first, in this order and label like this:

Weighted Average:

Median value from the weighted average problem:

Geometric Mean Return:

What would be the value of $1,200:

And then explain the difference between weighted average and geometric mean.

Answer 1

Weighted average:

Weighted average, =[x.f(x)]/f(x) =[(5*25)+(20*11)+....+(100*1)]/(25+11+8+3+1) =(125+220+240+225+100)/48 =910/48 =$18.96

Median:

x	f(x)	Cumulative frequency
5	25	25
20	11	25+11 =36
30	8	36+8 =44
75	3	44+3 =47
100	1	47+1 =48
	48

f(x)/2 =48/2 =24

24 is less than the cumulative frequency of 25 where $5 is present.

Therefore, Median, M =$5

Geometric mean return:

Geometric mean return, GM =[(15)(-20)(30)(-8)(25)]1/5 =17.8260%

Future VALUE (FV) of $1200:

FV =PV(1+r)n

Let the rate of interest, r =10% =0.10

Given: n =5 years; Present value, PV =$1200

Thus, FV =1200(1+0.10)5 =$1932.61

Answers:

Weighted Average: $18.96

Median value from the weighted average problem: $5

Geometric Mean Return: 17.8260%

What would be the value of $1,200: $1932.61