Question

Heavy football players: Following are the weights, in pounds, for samples of offensive and defensive linemen on a professional football team at the beginning of a recent year.

Offense:	289	337	275	269	263	291	321	352	279	270	269	302
Defense:	250	290	273	355	275	320	320	333	360	345	259	334

(a) Find the sample standard deviation for the weights for the offensive linemen. Round the answer to at least one decimal place.

The sample standard deviation for the weights for the offensive linemen is lb .

(b) Find the sample standard deviation for the weights for the defensive linemen. Round the answer to at least one decimal place.

The sample standard deviation for the weights for the defensive linemen is lb .

Answer 1

a.
given data,
Offense:  
289 337 275 269 263 291 321 352 279 270 269 302
Defense:  
250 290 273 355 275 320 320 333 360 345 259 334

Mean = Sum of observations/ Count of observations
Mean = (289 + 337 + 275 + 269 + 263 + 291 + 321 + 352 + 279 + 270 + 269 + 302 / 12) = 293.0833
Variance
Step 1: Add them up
289 + 337 + 275 + 269 + 263 + 291 + 321 + 352 + 279 + 270 + 269 + 302 = 3517
Step 2: Square your answer
3517*3517 =12369289
…and divide by the number of items. We have 12 items , 12369289/12 = 1030774.0833
Set this number aside for a moment.
Step 3: Take your set of original numbers from Step 1, and square them individually this time
289^2 + 337^2 + 275^2 + 269^2 + 263^2 + 291^2 + 321^2 + 352^2 + 279^2 + 270^2 + 269^2 + 302^2 = 1040177
Step 4: Subtract the amount in Step 2 from the amount in Step 3
1040177 - 1030774.0833 = 9402.9167
Step 5: Subtract 1 from the number of items in your data set, 12 - 1 = 11
Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance
9402.9167 / 11 = 854.8106
Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation
29.2371

b.
Mean = Sum of observations/ Count of observations
Mean = (250 + 290 + 273 + 355 + 275 + 320 + 320 + 333 + 360 + 345 + 259 + 334 / 12) = 309.5
Variance
Step 1: Add them up
250 + 290 + 273 + 355 + 275 + 320 + 320 + 333 + 360 + 345 + 259 + 334 = 3714
Step 2: Square your answer
3714*3714 =13793796
…and divide by the number of items. We have 12 items , 13793796/12 = 1149483
Set this number aside for a moment.
Step 3: Take your set of original numbers from Step 1, and square them individually this time
250^2 + 290^2 + 273^2 + 355^2 + 275^2 + 320^2 + 320^2 + 333^2 + 360^2 + 345^2 + 259^2 + 334^2 = 1165730
Step 4: Subtract the amount in Step 2 from the amount in Step 3
1165730 - 1149483 = 16247
Step 5: Subtract 1 from the number of items in your data set, 12 - 1 = 11
Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance
16247 / 11 = 1477
Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation
38.4318

Answer:
a.

the sample standard deviation for the weights for the offensive linemen =29.2371
b.
the sample standard deviation for the weights for the defensive linemen =38.4318