Question

Like hurricanes and earthquakes, geomagnetic storms are natural hazards with possible severe impact on the Earth. Severe storms can cause communication and utility breakdowns, leading to possible blackouts. The National Oceanic and Atmospheric Administration beams electron and proton flux data in various energy ranges to various stations on the Earth to help forecast possible disturbances. The following are 25 readings of proton flux in the 47-68 kEV range (units are in p / (cm2-sec-ster-MeV)) on the evening of ecember 28, 2011:2310, 2320, 2010, 10800, 2190, 3360, 5640, 2540, 3360, 11800, 2010, 3430, 10600, 7370, 2160, 3200, 2020, 2850, 3500, 10200, 8550, 9500, 2260, 7730, 2250(a) Find a point estimate of the mean proton flux in this time period.(b) Find a point estimate of the standard deviation of the proton flux in this time period.(c) Find an estimate of the standard error of the estimate in part (a).

Answer 1

a) Mean = 4958.4 p / (cm²-sec-ster-MeV)

b) Standard deviation = 3420.45 p / (cm²-sec-ster-MeV)

c) Standard error = 684.09 p / (cm²-sec-ster-MeV)

Explanation:

Data:

2310, 2320, 2010, 10800, 2190, 3360, 5640, 2540, 3360, 11800, 2010, 3430, 10600, 7370, 2160, 3200, 2020, 2850, 3500, 10200, 8550, 9500, 2260, 7730, 2250

Sum = 123,960

Number of observations, n = 25

a) Mean =
`\frac{\textup{Sum of all observations}}{\textup{Total number of observations}}`

or

Mean =
`\frac{\textup{123,960}}{\textup{25}}`

or

Mean = 4958.4 p / (cm²-sec-ster-MeV)

data data-mean (data - mean)²

----------------------------------------------------------------

2310 -2648.4 7014022.56

2320 -2638.4 6961154.56

2010 -2948.4 8693062.56

10800 5841.6 34124290.56

2190 -2768.4 7664038.56

3360 -1598.4 2554882.56

5640 681.6 464578.56

2540 -2418.4 5848658.56

3360 -1598.4 2554882.56

11800 6841.6 46807490.56

2010 -2948.4 8693062.56

3430 -1528.4 2336006.56

10600 5641.6 31827650.56

7370 2411.6 5815814.56

2160 -2798.4 7831042.56

3200 -1758.4 3091970.56

2020 -2938.4 8634194.56

2850 -2108.4 4445350.56

3500 -1458.4 2126930.56

10200 5241.6 27474370.56

8550 3591.6 12899590.56

9500 4541.6 20626130.56

2260 -2698.4 7281362.56

7730 2771.6 7681766.56

2250 -2708.4 7335430.56

====================================

∑(Data - Mean)² = 280,787,736

====================================

Standard deviation =
`\sqrt\frac{\sum{(Data -mean)^2}}{n-1}`

or

Standard deviation =
`\sqrt(280,787,736)/(25-1)`

or

Standard deviation = 3420.45 p / (cm²-sec-ster-MeV)

c) Standard error =
`\frac{\textup{standard deviation}}{√(n)}`

or

Standard error =
`\frac{\textup{3420.45 }}{√(25)}`

or

Standard error = 684.09 p / (cm²-sec-ster-MeV)