Answer:
Mean = 31.22
Midrange = 28.50
Geometric mean = 28.74
Trimmed mean = 31.56
Step-by-step explanation:
Given the data :
39 41 25 17 48 29 31 17 24 36 17 24 40 38 42 11 43 47 27 25 17 23 43 20 32 48 26 26 9 46 44 44
Ordered data :
9, 11, 17, 17, 17, 17, 20, 23, 24, 24, 25, 25, 26, 26, 27, 29, 31, 32, 36, 38, 39, 40, 41, 42, 43, 43, 44, 44, 46, 47, 48, 48
The mean, xbar :
Xbar = Σx / n = 999 / 32 = 31.22
The midrange : (maximum - minimum) / 2
Midrange = (48 + 9) / 2 = 57 / 2 = 28.5
Geometric mean :
(x1*x2*.. xn)^1/n
Geometric mean = (x1*x2*.. xn)^1/32 = 28.74
24% trimmed mean :
24% of 32 = 0.24 * 32 = 7.68 ; this mean cutting off 8 values from the top and bottom and calculating the mean of the remaining values.
Data left :
24, 24, 25, 25, 26, 26, 27, 29, 31, 32, 36, 38, 39, 40, 41, 42
Σx / n = 505 / 16 = 31.5625
Trimmed mean = 31.56
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