Samples sample mean {61,62,63,64} 62.5 {61,62,63,65} 62.75 {61,62,63,66} 63 {61,62,63,67} 63.25 {61,62,64,65} 63 {61,62,64,66} 63.25 {61,62,64,67} 63.5 {61,62,65,66} 63.5 {61,62,65,67} 63.75 {61,62,66,67} 64 {61,63,64,65} 63.25 {61,63,64,66} 63.5 {61,63,64,67} 63.75 {61,63,65,66} 63.75 {61,63,65,67} 64 {61,63,66,67} 64.25 {61,64,65,66} 64 {61,64,65,67} 64.25 {61,64,66,67} 64.5 {61,65,66,67} 64.75 {62,63,64,65} 63.5 {62,63,64,66} 63.75 {62,63,64,67} 64 {62,63,65,66} 64 {62,63,65,67} 64.25 {62,63,66,67} 64.5 {62,64,65,66} 64.25 {62,64,65,67} 64.5 {62,64,66,67} 64.75 {62,65,66,67} 65 {63,64,65,66} 64.5 {63,64,65,67} 64.75 {63,64,66,67} 65 {63,65,66,67} 65.25 {64,65,66,67 65.5 Values frequency probability 1 62.5 1 1/35 2 62.75 1 1/35 3 63 2 2/35 4 63.25 3 3/35 5 63.5 4 4/35 6 63.75 4 4/35 7 64 5 5/35 8 64.25 4 4/35 9 64.5 4 4/35 10 64.75 3 3/35 11 65 2 2/35 12 65.25 1 1/35 13 65.5 1 1/35 Sum 35 1 FOR SAMPLE Mean = (62.5*1+62.75*1+63*2+63.25*3+63.5*4+63.75*4+64*5+64.25*4+64.5*4+64.75*3+65*2+65.25*1+65.5*1)/35 = 64 E(X2) =(62.52*1+62.752*1+632*2+63.252*3+63.52*4+63.752*4+642*5+64.252*4+64.52*4+64.752*3+652*2+65.252*1+65.52*1)/35 = 4096.5 Standard deviation =√4096.5-(64^2) = √0.5 = 0.707106 or 0.71 FOR POPULATION mean mean= 61.56 Standard deviation =√ 3798.4-(61.56^2) = 2.9608 Activity: 1. Find the best point estimate of the population mean.
|
Samples |
sample |
|
{61,62,63,64} |
62.5 |
|
{61,62,63,65} |
62.75 |
|
{61,62,63,66} |
63 |
|
{61,62,63,67} |
63.25 |
|
{61,62,64,65} |
63 |
|
{61,62,64,66} |
63.25 |
|
{61,62,64,67} |
63.5 |
|
{61,62,65,66} |
63.5 |
|
{61,62,65,67} |
63.75 |
|
{61,62,66,67} |
64 |
|
{61,63,64,65} |
63.25 |
|
{61,63,64,66} |
63.5 |
|
{61,63,64,67} |
63.75 |
|
{61,63,65,66} |
63.75 |
|
{61,63,65,67} |
64 |
|
{61,63,66,67} |
64.25 |
|
{61,64,65,66} |
64 |
|
{61,64,65,67} |
64.25 |
|
{61,64,66,67} |
64.5 |
|
{61,65,66,67} |
64.75 |
|
{62,63,64,65} |
63.5 |
|
{62,63,64,66} |
63.75 |
|
{62,63,64,67} |
64 |
|
{62,63,65,66} |
64 |
|
{62,63,65,67} |
64.25 |
|
{62,63,66,67} |
64.5 |
|
{62,64,65,66} |
64.25 |
|
{62,64,65,67} |
64.5 |
|
{62,64,66,67} |
64.75 |
|
{62,65,66,67} |
65 |
|
{63,64,65,66} |
64.5 |
|
{63,64,65,67} |
64.75 |
|
{63,64,66,67} |
65 |
|
{63,65,66,67} |
65.25 |
|
{64,65,66,67 |
65.5 |
|
|
Values |
frequency |
probability |
|
1 |
62.5 |
1 |
1/35 |
|
2 |
62.75 |
1 |
1/35 |
|
3 |
63 |
2 |
2/35 |
|
4 |
63.25 |
3 |
3/35 |
|
5 |
63.5 |
4 |
4/35 |
|
6 |
63.75 |
4 |
4/35 |
|
7 |
64 |
5 |
5/35 |
|
8 |
64.25 |
4 |
4/35 |
|
9 |
64.5 |
4 |
4/35 |
|
10 |
64.75 |
3 |
3/35 |
|
11 |
65 |
2 |
2/35 |
|
12 |
65.25 |
1 |
1/35 |
|
13 |
65.5 |
1 |
1/35 |
|
Sum |
|
35 |
1 |
FOR SAMPLE
Mean =
(62.5*1+62.75*1+63*2+63.25*3+63.5*4+63.75*4+64*5+64.25*4+64.5*4+64.75*3+65*2+65.25*1+65.5*1)/35
= 64
E(X2)
=(62.52*1+62.752*1+632*2+63.252*3+63.52*4+63.752*4+642*5+64.252*4+64.52*4+64.752*3+652*2+65.252*1+65.52*1)/35
= 4096.5
Standard deviation
=√4096.5-(64^2)
= √0.5
= 0.707106 or 0.71
FOR POPULATION
mean
mean= 61.56
Standard deviation
=√ 3798.4-(61.56^2)
= 2.9608
Activity:
1. Find the best point estimate of the population mean.
Step by step
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