Box and Whisker Plots: - St. Francis Preparatory School



Box-and-Whisker Plots:

The quartiles, together with the low and high data values give us a very useful Five Number Summary.

Five Number Summary:

1) Largest Value

2) Q1

3) Median

4) Q2

5) Highest Value

We use all five numbers to create a graphical sketch of the data called a box-and-whisker plot. These plots are a useful way to describe data for exploratory data analysis (EDA).

To Construct a Box-and-Whisker Plot:

1) Draw a horizontal scale to include the highest and lowest data values.

2) To the right of the scale draw a box from Q1 to Q3.

3) Include a solid line through the box at the median level.

4) Draw solid lines, called whiskers, from Q1 to the lowest value and from Q3 to the highest value.

Examples:

For each of the following, calculate a five number summary. Use this summary to construct a box-and- whisker plot:

1) 45 67 34 78 29 68 32 64 78 96 54 05 54 97 65 94 86 09 05 46 79 05 69 80 76 09 76 98 07 69

2) 64 39 75 86 34 57 64 37 60 38 92 14 83 74 97 29 37 43 97 98 72 49 87 39 84 79 82 37 49 83 74 98 32 74 74 93

3) 65 74 86 39 86 57 89 36 58 73 65 34 65 83 65 89 26 59 29 27 50 92 17 34 90 75 98 37

4) 653 566 983 264 365 634 587 463 587 364 587 436 589 236 573 458 969 693 879 234 654 395 834 957 605 724 953 975 749 759 837 943 759 370 573 495

5) 678 346 273 462 453 532 754 235 428 354 235 425 432 754 185 432 810 948 236 894 268 648 792

6) 632 784 926 344 286 487 639 189 641 291 567 891 586 158 606 578 465 407 589 475 190 560 916 160 156 855 663 465 345 634 654 653 982 569 346 983

7) 547 856 874 564 654 184 135 181 478 941 131 878 464 579 487 947 654 372 137 375 313 126 359 354 537 213 541 353 123 127 431 734 1279 4213 741 212

8) 6629 6348 3146 3298 6482 3156 2856 8468 3268 5682 5634 6582 4365 3265 7836 4665 4365 8694 5684 3656 4685 6465 3865 4365 7863 8563 8463 6587 3645 6874 3657 8236 5843 6587 3625 6385 6392 8563 4652 6343 6765 9365 8766 7465 8743 6583 6584 3656 4367 6686 8764 8635 8965 3844 4444 7535 4353

We can also use the calculator to construct box-and-whisker plots:

1) Enter the data values into a list.

2) Turn Plot 1 ON and select the diagram that looks like a box-and-whisker plot.

3) Select ZOOM 9 to view the plot.

4) Select TRACE to see your 5 number summary.

Try these examples using the TI-83:

1) 62 39 86 43 82 65 78 23 46 58 47 83 26 57 34 65 62 53 64 56 43 65 76 34 56 38 26 59 36 54 62 58 29 64 53 57 23 58 43 26 96 26 66 57 63 45 23 65

2) 768 296 587 964 969 483 654 658 569 236 534 693 653 298 659 465 326 590 912 078 993 218 075 098 570 397 597 947 598 753 275 107 074 309 874 594 738 787 937 210 710 710 674 896 037 280 763 073 534 523 563 535 635 436 535 435 433 533 334 535 634 535 435 635 634 652

3) 464 896 642 356 835 683 568 364 583 658 396 487 365 863 462 892 369 265 326 926 262 658 346 292 675 857 943 209 573 407 531

4) 4678 2698 4634 3289 6472 9634 8976 2374 6289 4665 8756 4365 8453 6926 4658 3465 3465 3465 8464 3654 3646 6548 4638 6546 3667 6366 5784 6364 6587 3682 9463 4789 3652

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