Question

use the following data, which represent the english placement test scores of a sample of 30 students, to construct a frequency distribution with a first class of 472-492.

537, 526, 478, 541, 581
491, 497, 561, 494, 485
552, 566, 517, 548, 513
574, 480, 497, 472, 541
570, 550, 586, 576, 491
513, 527, 490, 521, 563

placement test scores	number of students
493-513
514-534
535-555
556-576
577-597

Explanation:

⚡ Using what you learned: Organizing Data in Tables

Step 1: Sort the raw data

To accurately count the frequencies for each class, we first list the 30 data points in ascending order:

\[
472, 478, 480, 485, 490, 491, 491, 494, 497, 497, 513, 513, 517, 521, 526, 527, 537, 541, 541, 548, 550, 552, 561, 563, 566, 570, 574, 576, 581, 586
\]

Step 2: Count frequencies for each class interval

• Class \(472 - 492\):

Values: \(472, 478, 480, 485, 490, 491, 491\)
Count: \(7\)

• Class \(493 - 513\):

Values: \(494, 497, 497, 513, 513\)
Count: \(5\)

• Class \(514 - 534\):

Values: \(517, 521, 526, 527\)
Count: \(4\)

• Class \(535 - 555\):

Values: \(537, 541, 541, 548, 550, 552\)
Count: \(6\)

• Class \(556 - 576\):

Values: \(561, 563, 566, 570, 574, 576\)
Count: \(6\)

• Class \(577 - 597\):

Values: \(581, 586\)
Count: \(2\)

Step 3: Verify total count

\[
7 + 5 + 4 + 6 + 6 + 2 = 30
\]

The sum matches the sample size of 30 students.

Answer:

Placement Test Scores	Number of Students
493–513	5
514–534	4
535–555	6
556–576	6
577–597	2