Question

A class of 37 students took a test worth 100 points. The five-number summary of their scores is 55, 67, 73, 81, 98. Identify the FALSE statement: Group of answer choices At least 25% of the students scored a 67 or below. At least 18 students scored below a 67. At least 9 students scored between 67 and 73. At least 25% of the students scored an 81 or above.

Answer 1

At least 18 students scored below a 67.

Explanation:

Given the 5 number summary of scores obtained by 37 students in a test worth 100 points :

55, 67, 73, 81, 98

Minimum = 55

Q1 = 67

Q2 = 73

Q3 = 81

Maximum = 98

Q1 = first quartile = 25%

Atleast 25 % scored below 67 (True)

25% of 37 students = 0.25 * 37 = 9.25

Atleast 9 students scored below 67 (True)

Median, Q2 = 50%

Score between Q2 and Q1 = 50% - 25% = 25% ;

Hence, atleast 25 students scored between 73 and 67 ; meaning (0.25 *37) = 9.25 students Hence. Atleast, 9 students scored between 73 and 67 (True)

Third quartile = 75%

Percentage above third quarterile = (100 - 75)% = 25%

Hence, atleast 25% scored above 81 (True)

The false statement is At least 18 students scored below a 67.