Statistics – Construct a frequency distribution and histogram using classes

by | Jun 5, 2025 | Business

The following table lists the average math SAT scores for each state for the year 2009.
State SAT State SAT
Alabama 552 Montana 542
Alaska 516 Nebraska 594
Arizona 521 Nevada 505
Arkansas 572 New Hampshire 523
California 513 New Jersey 513
Colorado 575 New Mexico 546
Connecticut 513 New York 502
Delaware 498 North Carolina 511
Florida 498 North Dakota 593
Georgia 491 Ohio 546
Hawaii 502 Oklahoma 571
Idaho 540 Oregon 525
Illinois 604 Pennsylvania 501
Indiana 507 Rhode Island 496
Iowa 615 South Carolina 496
Kansas 589 South Dakota 600
Kentucky 573 Tennessee 565
Louisiana 558 Texas 506
Maine 467 Utah 558
502 Vermont 518
Massachusetts 526 Virginia 512
Michigan 603 Washington 531
Minnesota 609 West Virginia 501
Mississippi 554 Wisconsin 608
Missouri 600 Wyoming 568
SOURCE: www.collegeboard.com.
Click here for the Excel Data File
a-1. Construct a frequency distribution and histogram using classes of 450 to 500, 501 to 550, etc.
SAT Scores Frequency
450 – 500
501 – 550
551 – 600
601 – 650
Total
a-2. How many of the states had scores between 551 and 600?
Number of states
b.

Construct the relative frequency, the cumulative frequency, and the cumulative relative frequency distributions. (Round “Relative Frequency” and “Cumulative Relative Frequency” to 2 decimal places.)
SAT Scores Relative
Frequency		 Cumulative
Frequency		 Cumulative
Relative
Frequency
450 – 500
501 – 550
551 – 600
601 – 650
Total
c. How many of the states had math SAT scores of 550 or less?
Number of states
d-1. What percent of the states had math SAT scores between 551 and 600? (Round your answer to the nearest whole percent.)
Percent of states
d-2.

What percent of the states had mean SAT scores of 550 or less? (Round your answer to the nearest whole percent.)
Percent of states

References WorksheetLearning Objective: 02-03 Summarize quantitative data by forming frequency distributions.Difficulty: 3 HardLearning Objective: 02-04 Construct and interpret histograms, polygons, and ogives.

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