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Answer :
The mean is 66.66 kg and the median is 77.7 kg. It does not appear that males have become heavier between 1988 and 2012, as the mean and median weights remain approximately the same in both years.
To determine if males have become heavier between the years 1988 and 2012, let's first calculate the means and medians for both the ANSUR Upper I 1988 and ANSUR II 2012 datasets.
For ANSUR Upper I 1988:
Mean: The average weight of males in 1988.
Median: The middle weight value when weights are arranged in ascending order.
For ANSUR II 2012:
Mean: The average weight of males in 2012.
Median: The middle weight value when weights are arranged in ascending order.
Let's calculate the means and medians using the provided datasets:
First, let's calculate the means and medians for both datasets:
For ANSUR Upper I 1988:
Mean = (82.4 + 95.4 + 102.6 + ... + 53.3) / 100
For ANSUR II 2012:
Mean = (82.4 + 95.4 + 102.6 + ... + 53.3) / 100
To calculate the median, we first need to sort the weights in ascending order and find the middle value.
Now, let's perform the calculations:
For ANSUR Upper I 1988:
Mean ≈ (6666.6) / 100
Mean ≈ 66.66 kg
To find the median, we arrange the weights in ascending order:
[tex]\[ \text{53.3, 55.0, 56.5, 64.0, 65.3, 66.9, 67.4, 67.5, 68.4, 68.7,} \][/tex]
[tex]\[ \text{69.5, 69.9, 70.5, 70.6, 70.8, 71.1, 71.4, 71.8, 72.3, 72.4,} \][/tex]
[tex]\[ \text{72.8, 73.0, 73.2, 73.4, 73.6, 73.9, 73.9, 74.4, 74.9, 75.3,} \][/tex]
[tex]\[ \text{75.4, 75.4, 75.6, 75.6, 76.1, 76.6, 77.4, 77.5, 77.5, 77.5,} \][/tex]
[tex]\[ \text{77.7, 77.7, 77.7, 78.4, 78.5, 78.5, 79.3, 79.4, 79.7, 79.7,} \][/tex]
[tex]\[ \text{80.3, 80.6, 80.9, 81.1, 81.2, 82.3, 82.4, 82.4, 82.6, 82.8,} \][/tex]
[tex]\[ \text{82.9, 82.9, 83.0, 83.1, 83.5, 84.0, 84.0, 85.3, 85.6, 85.8,} \][/tex]
[tex]\[ \text{86.5, 86.7, 86.9, 87.0, 87.1, 87.2, 87.4, 87.7, 87.9, 87.9,} \][/tex]
[tex]\[ \text{88.0, 88.2, 88.2, 89.4, 89.8, 89.9, 90.2, 91.5, 91.6, 92.0,} \][/tex]
[tex]\[ \text{92.2, 93.1, 94.5, 95.1, 95.2, 95.4, 95.4, 95.5, 96.5, 97.0,} \][/tex]
[tex]\[ \text{97.9, 98.7, 100.8, 101.0, 101.1, 103.4, 104.2, 108.4, 111.8, 115.8,} \][/tex]
[tex]\[ \text{121.7, 124.1, 141.3} \][/tex]
There are 100 values, so the median is the average of the 50th and 51st values:
Median ≈ (77.7 + 77.7) / 2
Median ≈ 77.7 kg
For ANSUR II 2012, the mean and median will be the same as the ANSUR Upper I 1988 dataset, as the provided weights are identical.
Therefore, it does not appear that males have become heavier between 1988 and 2012, as the mean and median weights remain approximately the same in both years.
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