Because the mean is very sensitive to extreme values, it is not a resistant meas

Question

Because the mean is very sensitive to extreme values, it is not a resistant measure of center. The trimmed mean is more resistant. To find the 10% trimmed mean for a data set. fast arrange the data in order, then delete the bottom 10% of the values and the top 10% of the values, then calculate tt mean of the remaining values For the following credit-rating scores, find (a) the mean, (b) the 10% trimmed mean, and (c) the 20% trimmed mean. How do the results compare? The 10% trimmed mean is (Round to one decimal place as needed) The 20% trimmed mean is (Round to one decimal place as needed) How do the results compare? The distribution of the data may be skewed to the light because the mean appears to decrease slightly as values are trimmed There is zero skew in the distribution of the data because the three means are almost exactly equal. The distribution of the data may be skewed to the left because the mean appeals to increase slightly as values are trimmed.

Explanation / Answer

Arrange the data in an ascending order:

337, 558, 614, 660, 682, 701,702, 708, 712, 713, 738, 750, 764, 765, 778, 787, 788, 795, 804, 833

b. To find 10% trimmed mean trim 10% data from top and bottom.

Here n=20, p=0.10, hence k=np=20*0.10=2

The remaining values are:

614, 660, 682, 701,702, 708, 712, 713, 738, 750, 764, 765, 778, 787, 788, 795

The 10% trimmed mean is:

1/16*(614+660+…+795)

=728.56

e. To find 20% trimmed mean trim 20% data from top and bottom.

Here n=20, p=0.20, hence k=np=20*0.20=4

The remaining values are:

682, 701,702, 708, 712, 713, 738, 750, 764, 765, 778, 787

The 20% trimmed mean is:

1/12*(682+701+…+787)

=733.33

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