Question Continuation
a. Compute the mean measurement for each method.
b. Compute the median measurement for. each method.
c. Compute the 20% trimmed mean measurement for each method.
Answer:
a. Mean
Mean A = 22.675
Mean B = 20.71875
Mean C = 21.0125
Mean D = 20.86875
b. Median
Median A = 23.45
Median B = 20.45
Median C = 21.0
Median D = 20.7
c. 20% Trimmed Mean
Trimmed Mean A = 23.14
Trimmed Mean B = 20.73
Trimmed Mean C = 21.04
Trimmed Mean D = 20.75
Explanation:
a.
Mean = Σx/n
Where Σx= Summation of entries in each method
n = 16
Mean of Method A = (18.0 + 18.0 +18.0 + 19.0 + 22.0 + 22.0 + 22.5 + 22.9 + 24.0 + 24.0 + 25.0 +25.0 + 25.0 + 25.0 + 26.0 +26.4)/16
Mean A = 362.8/16
Mean A = 22.675
Mean of Method B = (18.8 + 18.9 + 18.9 + 19.8 + 20.1 + 20.4 + 20.4 + 20.4 + 20.6 + 20.5 + 21.2 + 21.9 + 22.0 + 22.0 + 22.0 + 23.6)16
Mean B = 331.5/16
Mean B = 20.71875
Mean of Method C = (20.2 + 20.5 + 20.5 + 20.7 + 20.8 + 20.9 + 21.0 + 21.0 + 21.0 + 21.0 + 21.0 + 21.5 + 21.5 + 21.5 + 21.5 + 21.6)/16
Mean C = 336.2/16
Mean C = 21.0125
Mean of Method D = (20.0 + 20.0 + 20.0 + 20.2 + 20.2 + 20.5 + 20.5 + 20.7 + 20.7 + 20.7 + 21.0 + 21.5 + 21.5 + 21.6 + 22.1 + 22.3)/16
Mean D = 333.9/16
Mean D = 20.86875
b.
Median is the number(s) at the middle
Since the total number of points for each method is 16 and this is an even number we need to calculate the median as the average between the 8th and the 9th position of the data ordered from the smallest to the largest. If we do this we have that:
Method A
Arranged Data: 18.0, 18.0, 18.0, 19.0, 22.0, 22.0, 22.5, 22.9, 24.0, 24.0, 25.0, 25.0, 25.0, 25.0, 26.0, 26.4
The 8th and 9th data are: 22.9 and 24.0
Median = (22.9 + 24.0/2
Median = 46.9/2
Median A = 23.45
Method B
Arranged Data: 18.8, 18.9, 18.9, 19.8, 20.1, 20.4, 20.4, 20.4, 20.5, 20.6, 21.2, 21.9, 22.0, 22.0, 22.0, 23.6
The 8th and 9th data are: 20.4 and 20.5
Median = (20.4+20.5)/2
Median = 40.9/2
Median B = 20.45
Method C
Arranged Data: 20.2, 20.5, 20.5, 20.7, 20.8, 20.9, 21.0, 21.0, 21.0, 21.0, 21.0, 21.5, 21.5, 21.5, 21.5, 21.6
The 8th and 9th data are: 21.0 and 21.0
Median = (21.0 + 21.0)/2
Median = 42.0/2
Median C = 21.0
Method D
Arranged Data: 20.0, 20.0, 20.0, 20.2, 20.2, 20.5, 20.5, 20.7, 20.7, 20.7, 21.0, 21.5, 21.5, 21.6, 22.1, 22.3
The 8th and 9th data are: 20.7 and 20.7
Median = (20.7+20.7)/2
Median = 41.4/2
Median D = 20.7
c.
The trimmed mean by 20% means that we'll calculate mean by removing the 20% from each of the tails.
20% of 16 = 3.2 (Approximated to 3)
So we need to remove 3 observations from both ends of the data.
Method A becomes
19.0, 22.0, 22.0, 22.5, 22.9, 24.0, 24.0, 25.0, 25.0, 25.0
Trimmed Mean A = (19.0+22.0+22.0+22.5+ 22.9+24.0+24.0+25.0+ 25.0+ 25.0)/10
Trimmed Mean A = 231.4/10
Trimmed Mean A = 23.14
Method B becomes
19.8, 20.1, 20.4, 20.4, 20.4, 20.6, 20.5, 21.2, 21.9, 22.0
Trimmed Mean B = (19.8+20.1+20.4+ 20.4+ 20.4+20.6+20.5+21.2+21.9+22.0)/10
Trimmed Mean B = 207.3/10
Trimmed Mean B = 20.73
Method C becomes
20.7, 20.8, 20.9, 21.0, 21.0, 21.0, 21.0, 21.0, 21.5, 21.5
Trimmed Mean C = (20.7+ 20.8+ 20.9+ 21.0+ 21.0+ 21.0+21.0+, 21.0+, 21.5+21.5)/10
Trimmed Mean C = 210.4/10
Trimmed Mean C = 21.04
Method D becomes
20.2, 20.2, 20.5, 20.5, 20.7, 20.7, 20.7, 21.0, 21.5, 21.5
Trimmed Mean D = (20.2+, 20.2+20.5+, 20.5+ 20.7+ 20.7+ 20.7 +, 21.0 +21.5 + 21.5)/10
Trimmed Mean D = 207.5/10
Trimmed Mean D = 20.75
