Homework SourseBased on the given data what proportion of the math scores f
Based on the given data, what proportion of the math scores falls within 2 standard deviation of the mean?
| 513 |
| 494 |
| 517 |
| 520 |
| 504 |
| 508 |
| 543 |
| 492 |
| 494 |
| 457 |
| 486 |
| 508 |
| 496 |
| 453 |
| 513 |
| 543 |
| 482 |
| 401 |
| 524 |
| 517 |
| 487 |
| 491 |
| 459 |
| 485 |
| 476 |
| 500 |
| 523 |
| 421 |
| 487 |
| 470 |
Solution
Based on the given data, what proportion of the math scores falls within 2 standard deviation of the mean?
Sorted data
401
421
453
457
459
470
476
482
485
486
487
487
491
492
494
494
496
500
504
508
508
513
513
517
517
520
523
524
543
543
N
30
mean
492.13
sample standard deviation
31.61
Mean -2*sd = 492.13-2*31.61 = 428.9
Mean +2*sd = 492.13+2*31.61 = 555.4
There are 28 observations of the math scores falls within 2 standard deviation of the mean.
The required proportion = 28/30 =0.9333
| 401 |
| 421 |
| 453 |
| 457 |
| 459 |
| 470 |
| 476 |
| 482 |
| 485 |
| 486 |
| 487 |
| 487 |
| 491 |
| 492 |
| 494 |
| 494 |
| 496 |
| 500 |
| 504 |
| 508 |
| 508 |
| 513 |
| 513 |
| 517 |
| 517 |
| 520 |
| 523 |
| 524 |
| 543 |
| 543 |
