For the following data set: 3 18 22 38 42 51 63 79 (a) Compute the 12.5% trimmed

Question

For the following data set: 3 18 22 38 42 51 63 79 (a) Compute the 12.5% trimmed mean. Round your answer to three decimal places. 12.5% trimmed mean = 39 (b) Compute the 25% trimmed mean. Round your answer to three decimal places 25% trimmed mean = 38.25 (c) Use linear interpolation to find the 18.75% trimmed mean. Round your answer to three decimal places. Hint: 18.75 is the average of 12.5 and 25. 18.75% trimmed mean 38.625 (d) Use linear interpolation to findthe 20% trimmed mean Round your answer to three decimal places 20% trimmed mean = Enter a number

Explanation / Answer

d) 20% trimmed mean is rejecting 1.6 entries from either side. Since we need to do the linear interpolation, we know from a and b that 12.5% trimmed mean rejects 1 from either side, and 25% trimmed mean rejects 2 from either side. We need to find a linear combination of 1 and 2 to get 1.6.

Let w<1 be the weight. We need w such that

1*w+(1-w)*2 = 1.6

or

2-w=1.6

or w=0.4

the trimmed mean for 12.5% is 39 and trimmed mean for 25% is 38.25. Hence the trimmed mean for 20% with interpolation is

39*0.4+38.25*(1-0.4) = 38.55

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