Question

.W 3. The state average SAT Critical Reading scores, ordered from smallest to largest, appear below. 469 469 479 479 482 485 485 487 489 493 493 493 494495 495 499 499 509 512 513 514 515 515 517 520 523523 539 539 542 546 548 555 563 564 568 570 571 572575 576 580 583 584 585 586 590 592 593 596 599 a. Determine a five-number summary of the state average SAT Critical Reading scores. b. Does California (average score 499) fall in the top half of the states in the SAT Critical Reading score? Does it fall above the bottom quarter? Support your answer. c. Roughly what percentage of the states have scores higher than Wyoming's 572? How many states would that be? d. Make a basic boxplot of the states' average SAT Critical Reading scores. Which quarter of the data, the first, second, third or fourth, shows the most amount of spread?

Answer 1

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(a) Five Number Summary, statistics are : (i) Minimum (heast value) (ii) First Quartile (Q, = strth item ) (i) Second Quartile CQ2 = Alerts item) (iv) Third Quartile (Q₂ = 30 item) (1) Maximum (hargest Value) 4

@,= ($1+1 )" item = 13th item = 494 · Q, = (51+1 jt item = 26" item = 523 3(5140) th item = 39"item = 572 Minimum Maximum = 469 = 599

(6.) It falls in the top half. since median (Middle part, 22) value is 5232 i California average score 499 is less than Median value (523) of. stat STAT Critical Reading Score. (C) N=51.. out of. 51,13 observations a (states) are higher than hiyoming's 572 Percentage - 13 x100 = 25.490% (d.) Box plot is shown below. From box plot it is clear that third quarted quarter Shows the most amount of Spread. the

Maximum Minimum Population size: 51 Median: 523 Minimum: 469 Maximum: 599 First quartile: 494 Third quartile: 572 Interquartile Range: 78 Outliers: none