To find the mean of the weights of the starting lineup of the football team, we need to sum all the weights and then divide by the number of weights.
The weights given are: 217, 235, 212, 253, 233, 171, 184, 301, 256, 297, 247, 226, 237, 241, 195, 204, 197, 214, 166, 309, 281, 303, 309, 299
First, let's sum all the weights:
\[ 217 + 235 + 212 + 253 + 233 + 171 + 184 + 301 + 256 + 297 + 247 + 226 + 237 + 241 + 195 + 204 + 197 + 214 + 166 + 309 + 281 + 303 + 309 + 299 \]
Calculating that step-by-step:
\[ 217 + 235 = 452 \] \[ 452 + 212 = 664 \] \[ 664 + 253 = 917 \] \[ 917 + 233 = 1150 \] \[ 1150 + 171 = 1321 \] \[ 1321 + 184 = 1505 \] \[ 1505 + 301 = 1806 \] \[ 1806 + 256 = 2062 \] \[ 2062 + 297 = 2359 \] \[ 2359 + 247 = 2606 \] \[ 2606 + 226 = 2832 \] \[ 2832 + 237 = 3069 \] \[ 3069 + 241 = 3310 \] \[ 3310 + 195 = 3505 \] \[ 3505 + 204 = 3709 \] \[ 3709 + 197 = 3906 \] \[ 3906 + 214 = 4120 \] \[ 4120 + 166 = 4286 \] \[ 4286 + 309 = 4595 \] \[ 4595 + 281 = 4876 \] \[ 4876 + 303 = 5179 \] \[ 5179 + 309 = 5188 \] \[ 5188 + 299 = 5487 \]
Now, the total weight is \( 5487 \) pounds.
Next, we need the number of weights. There are \( 24 \) weights.
Now we calculate the mean:
\[ \text{Mean} = \frac{\text{Total Sum}}{\text{Number of Weights}} = \frac{5487}{24} \]
Calculating the mean gives:
\[ \text{Mean} \approx 228.625 \]
Thus, the mean of the weights is approximately \( 228.63 \) pounds (rounded to two decimal places).
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