Question

The weights of the starting lineup of a football team are as follows (in pounds)
217 235 212 253 233 171 184 301 256 297 247 226 237 241 195 204 197 214 166 309 281 303 309 299 What is the mean of the data? (2 points)

Answer 1

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).