To find the mean and median weights for both offensive and defensive linemen, we will first compute the values for each group.
(a) Offensive Linemen
Weights: 329, 294, 311, 330, 312, 263, 326, 327, 301, 322, 259, 310
Mean: To calculate the mean, we first find the sum of all weights: \[ 329 + 294 + 311 + 330 + 312 + 263 + 326 + 327 + 301 + 322 + 259 + 310 = 3,712 \] Now, divide the sum by the number of data points (12): \[ \text{Mean} = \frac{3,712}{12} = 309.33 \text{ (rounded to 1 decimal place: 309.3)} \]
Median: To find the median, we need to first arrange the weights in ascending order: 259, 263, 294, 301, 310, 311, 312, 322, 326, 327, 330, 329
There are 12 weights (even number), so the median will be the average of the 6th and 7th values: \[ \text{Median} = \frac{311 + 312}{2} = \frac{623}{2} = 311.5 \]
(b) Defensive Linemen
Weights: 252, 283, 308, 291, 295, 258, 319, 283, 308, 279, 282, 318
Mean: Calculate the sum of the weights: \[ 252 + 283 + 308 + 291 + 295 + 258 + 319 + 283 + 308 + 279 + 282 + 318 = 3,413 \] Now, divide by the number of data points (12): \[ \text{Mean} = \frac{3,413}{12} = 284.42 \text{ (rounded to 1 decimal place: 284.4)} \]
Median: First, arrange the weights in ascending order: 252, 258, 279, 282, 283, 283, 291, 295, 308, 308, 318, 319
The 6th and 7th values are both 283 and 291: \[ \text{Median} = \frac{283 + 291}{2} = \frac{574}{2} = 287.0 \]
(c) Comparison
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Mean weight of offensive linemen: 309.3
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Median weight of offensive linemen: 311.5
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Mean weight of defensive linemen: 284.4
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Median weight of defensive linemen: 287.0
From the calculations:
- Offensive linemen tend to be heavier than defensive linemen, both in terms of mean weight and median weight.
Summary
- (a) Mean Offensive Weights: 309.3, Median: 311.5
- (b) Mean Defensive Weights: 284.4, Median: 287.0
- (c) Offensive linemen are heavier than defensive linemen.