In: Math

Below is a list of the profit or (loss) of 40 companies.

- Calculate the population parameters for all 40 companies profit or loss

- Select a sample of 10

- Calculate the point estimators of the sample

- Compare the results (Point estimators with Population Parameters)

**$ In Millions**

$9,862 $19,710

$44,940 $48,351

$10,558 $5,070

$6,662 $3,033

$29,450 ($3,864)

7,602 $364.5

$9,195 $1,288

$2,679 $30,101

$1,907 ($5786)

$4,078 $24,441

$2,463 $12,662

$8,630 $18,232

$4,517.4 $22,183

$8,197 $5,106

$3,842.8 $21,204

$4,065 $22,714

$2,997 $9,609

$246.5 $4,286

$3,577 $2,736

$2,421.9 $1,982

### Using Excel:

Data | X-mu | (X-mu)^2 | |

9862 | -653.33 | 426840.089 | |

9710 | -805.33 | 648556.409 | |

44940 | 34424.67 | 1185057905 | |

48351 | 37835.67 | 1431537924 | |

10558 | 42.67 | 1820.7289 | |

5070 | -5445.33 | 29651618.8 | |

6662 | -3853.33 | 14848152.1 | |

3033 | -7482.33 | 55985262.2 | |

29450 | 18934.67 | 358521728 | |

3864 | -6651.33 | 44240190.8 | |

7602 | -2913.33 | 8487491.69 | |

364.5 | -10150.8 | 103039350 | |

9195 | -1320.33 | 1743271.31 | |

1288 | -9227.33 | 85143618.9 | |

2679 | -7836.33 | 61408067.9 | |

30101 | 19585.67 | 383598469 | |

1907 | -8608.33 | 74103345.4 | |

5786 | -4729.33 | 22366562.2 | |

4078 | -6437.33 | 41439217.5 | |

24441 | 13925.67 | 193924285 | |

2463 | -8052.33 | 64840018.4 | |

12662 | 2146.67 | 4608192.09 | |

8630 | -1885.33 | 3554469.21 | |

18232 | 7716.67 | 59546995.9 | |

4517.4 | -5997.93 | 35975164.3 | |

22183 | 11667.67 | 136134523 | |

8197 | -2318.33 | 5374653.99 | |

5106 | -5409.33 | 29260851 | |

3842.8 | -6672.53 | 44522656.6 | |

21204 | 10688.67 | 114247666 | |

4065 | -6450.33 | 41606757.1 | |

22714 | 12198.67 | 148807550 | |

2997 | -7518.33 | 56525286 | |

9609 | -906.33 | 821434.069 | |

246.5 | -10268.8 | 105448870 | |

4286 | -6229.33 | 38804552.2 | |

3577 | -6938.33 | 48140423.2 | |

2736 | -7779.33 | 60517975.2 | |

2421.9 | -8093.43 | 65503609.2 | |

1982 | -8533.33 | 72817720.9 | |

Total | 420613.1 | 5233233045 | |

Mean | 10515.33 |

The population mean is given by:

The population standard deviation is given by:

## By using R command: We draw a random sample of size 10 from the given population.

>
data=c(9862,9710,44940,48351,10558,5070,6662,3033,29450,3864,7602,364.5,9195,1288,2679,30101,1907,5786,4078
,24441,2463 ,12662,8630
,18232,4517.4,22183,8197,5106,3842.8,21204,4065
,22714,2997,9609,246.5,4286,3577,2736,2421.9,1982)

> data

[1] 9862.0 9710.0 44940.0 48351.0 10558.0 5070.0 6662.0 3033.0
29450.0

[10] 3864.0 7602.0 364.5 9195.0 1288.0 2679.0 30101.0 1907.0
5786.0

[19] 4078.0 24441.0 2463.0 12662.0 8630.0 18232.0 4517.4 22183.0
8197.0

[28] 5106.0 3842.8 21204.0 4065.0 22714.0 2997.0 9609.0 246.5
4286.0

[37] 3577.0 2736.0 2421.9 1982.0

> x=sample(data,10)

> x

[1] 2463.0 12662.0 4517.4 4065.0 21204.0 5106.0 3033.0 9195.0
1288.0

[10] 8197.0

### By using excel:

Sample(x) | (x-xbar) | (x-xbar)^2 | |

2463 | -4710.04 | 22184477 | |

12662 | 5488.96 | 30128682 | |

4517.4 | -2655.64 | 7052423.8 | |

4065 | -3108.04 | 9659912.6 | |

21204 | 14030.96 | 196867839 | |

5106 | -2067.04 | 4272654.4 | |

3033 | -4140.04 | 17139931 | |

9195 | 2021.96 | 4088322.2 | |

1288 | -5885.04 | 34633696 | |

8197 | 1023.96 | 1048494.1 | |

Total | 71730.4 | 327076431 | |

xbar | 7173.04 |

The sample mean is given by:

The sample standard deviation is given by:

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