In this exercise you will compare the efficiency of the mean of a sample to thre

Question

In this exercise you will compare the efficiency of the mean of a sample to three other estimators of position of a continuous distribution in one coordinate. All three of the alternative estimators have the advantage of being more robust than the mean. N.B. Pay careful attention to the questions asked below as well as to the construction of the spreadsheet. Enter answers to the questions in some prominent place in the workbook. a) Using Excel, in one row generate ten Gaussian distributed random deviates with mean 0 and b) In the same row compute the mean of the ten deviates. c) In tho samc row computc tho mcdian of thc ton dcviatos. d) In the same row compute the "truncated mean" obtained by discarding the smallest and largest deviates and computing the mean of the remaining eight.

Explanation / Answer

First you generate the normal random variable with the help of data analysis toolpack. This generate the random variable easily. After this, we arrange the random number in decreasing form which can be do by sort & Filter. Then, find the mean, medain by selecting all values where as for truncated mean, we can easily calculated the mean because we arrange the data. Similarly for double truncated mean.

I have give starting the ten generating value which is

We can replicate this 3000 times and see

that

S.No.1 1 -0.83493 -1.93758 -1.53287 -1.85454 0.612083 -2.30477 -1.4226 -2.20743 -0.86746 2 -0.79914 -1.17805 -1.44549 -1.31945 -1.83648 -1.76819 -1.30713 -1.09016 -0.77857 3 -0.67399 -0.66461 -1.41569 -0.72997 -1.31635 -0.66022 -0.88113 -0.65273 -0.71083 4 -0.29352 -0.65282 -0.3261 -0.38519 -1.29306 -0.57612 -0.3782 -0.21801 -0.18662 5 0.098883 -0.1105 -0.14629 -0.17706 -1.06231 -0.34058 -0.26385 0.38882 0.096038 6 0.34951 0.187792 0.126367 0.207451 -0.68904 -0.14706 -0.04703 0.412028 0.292558 7 0.422795 0.224678 0.429665 0.352845 -0.46228 0.177913 -0.01419 0.464155 0.816742 8 0.552353 0.232844 0.432099 0.653674 0.584815 0.852726 0.056065 0.85515 0.853718 9 0.86101 0.916418 0.444056 1.247968 0.692048 1.233434 0.473719 1.074495 0.906452 10 1.441158 1.05201 1.417363 1.801291 1.60348 1.990729 0.544351 3.263995 2.200486 Mean 0.112414 -0.19298 -0.20169 -0.0203 -0.31671 -0.15421 -0.324 0.229031 0.262251 medain 0.224196 0.038648 -0.00996 0.015197 -0.57566 -0.24382 -0.15544 0.400424 0.194298 truncated mean 0.064738 -0.13053 -0.23767 -0.01872 -0.67283 -0.15351 -0.29522 0.154218 0.161185 double truncated 0.076006 -0.13043 -0.14999 -0.01304 -0.70637 -0.11556 -0.25472 0.208235 0.1936

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