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

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# 2.3 cont. Using the Mean and Standard Deviation Together - PowerPoint PPT Presentation

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

68-95-99.7 rule

z-scores

68-95-99.7 rule

Mean and

Standard Deviation

(numerical)

Histogram

(graphical)

68-95-99.7 rule

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.)

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.)

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.)

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
• 10
• 15
• 20
• 40

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### Z-scores: Standardized Data Values

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

Exam 1: y1 = 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
• 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.

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

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