2 3 cont using the mean and standard deviation together
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2.3 (cont.) Using the Mean and Standard Deviation Together. 68-95-99.7 rule z-scores. 68-95-99.7 rule. Mean and Standard Deviation (numerical). Histogram (graphical). 68-95-99.7 rule. The 68-95-99.7 rule; applies only to mound-shaped data.

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2 3 cont using the mean and standard deviation together

2.3 (cont.)Using the Mean and Standard Deviation Together

68-95-99.7 rule

z-scores


68 95 99 7 rule
68-95-99.7 rule

Mean and

Standard Deviation

(numerical)

Histogram

(graphical)

68-95-99.7 rule





Example textbook costs
Example: textbook costs

286 291 307 308 315 316 327 328 340 342 346 347 348 348 349 354 355 355 360 361 364 367 369 371 373 377 380 381 382 385 385 387 390 390 397 398 409 409 410 418 422 424 425 426 428 433 434 437 440 480


Example textbook costs cont
Example: textbook costs (cont.)

286 291 307 308 315 316 327 328 340 342 346 347 348 348 349 354 355 355 360 361 364 367 369 371 373 377 380 381 382 385 385 387 390 390 397 398 409 409 410 418 422 424 425 426 428 433 434 437 440 480


Example textbook costs cont1
Example: textbook costs (cont.)

286 291 307 308 315 316 327 328 340 342 346 347 348 348 349 354 355 355 360 361 364 367 369 371 373 377 380 381 382 385 385 387 390 390 397 398 409 409 410 418 422 424 425 426 428 433 434 437 440 480


Example textbook costs cont2
Example: textbook costs (cont.)

286 291 307 308 315 316 327 328 340 342 346 347 348 348 349 354 355 355 360 361 364 367 369 371 373 377 380 381 382 385 385 387 390 390 397 398 409 409 410 418 422 424 425 426 428 433 434 437 440 480


The best estimate of the standard deviation of the men s weights displayed in this dotplot is
The best estimate of the standard deviation of the men’s weights displayed in this dotplot is

  • 10

  • 15

  • 20

  • 40

7


Z scores standardized data values

Z-scores: Standardized Data Values weights displayed in this dotplot is

Measures the distance of a number from the mean in units of the standard deviation


Z score corresponding to y
z-score corresponding to y weights displayed in this dotplot is


  • Exam 1: y weights displayed in this dotplot is1 = 88, s1 = 6; exam 1 score: 91

    Exam 2: y2 = 88, s2 = 10; exam 2 score: 92

    Which score is better?


Comparing sat and act scores
Comparing SAT and ACT Scores weights displayed in this dotplot is

  • SAT Math: Eleanor’s score 680

    SAT mean =500 sd=100

  • ACT Math: Gerald’s score 27

    ACT mean=18 sd=6

  • Eleanor’s z-score: z=(680-500)/100=1.8

  • Gerald’s z-score: z=(27-18)/6=1.5

  • Eleanor’s score is better.


Z scores add to zero
Z-scores add to zero weights displayed in this dotplot is


In 2007-08 the mean tuition at 4-yr public colleges/universities in the U.S. was $6185 with a standard deviation of $1804. In NC the mean tuition was $4320. What is NC’s z-score?

  • 1.03

  • -1.03

  • 2.39

  • 1865

  • -1865

10


End of section 2 3
End of Section 2.3 colleges/universities in the U.S. was $6185 with a standard deviation of $1804. In NC the mean tuition was $4320. What is NC’s z-score?


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