Question

Fifteen students were registered in Section 1 and 15 students were registered in Section 2 of a research course. They took the same midterm exam, and their exam scores were distributed as follows: Section 1: 89, 56, 45, 78, 98, 45, 55, 77, 88, 99, 98, 97, 54, 34, 94 Section 2: 77, 88, 87, 67, 98, 87, 55, 77, 45, 44, 88, 99, 69, 67, 98 a. Calculate the mode, median, mean, range, variance, and standard deviation for both sections. Include your SPSS output below. (10 pts) b. Which section did better overall on the exam? Fully justify your answer using the concepts in W&G Chapter 3. (3 pts)

Answer 1

a)

For Section 1 -

Mode : 45 , 98

Median - 78

Mean - 73.8

Range - 65

Variance - 537.03

Standard Deviation - 23.17

For Section 2 -

Mode : 67 , 77 , 87 , 88 , 98

Median - 77

Mean - 76.4

Range - 55

Variance - 333.11

Standard Deviation - 18.25

b)

Section 2 did better overall on the exam

Explanation:

As given,

Section 1: 89, 56, 45, 78, 98, 45, 55, 77, 88, 99, 98, 97, 54, 34, 94

Section 2: 77, 88, 87, 67, 98, 87, 55, 77, 45, 44, 88, 99, 69, 67, 98

a)

For Section 1 -

Mode : 45 , 98

Median - 78

Mean - 73.8

Range - 65

Variance - 537.03

Standard Deviation - 23.17

For Section 2 -

Mode : 67 , 77 , 87 , 88 , 98

Median - 77

Mean - 76.4

Range - 55

Variance - 333.11

Standard Deviation - 18.25

b)

As,

Standard deviation of section 2 < Standard deviation of section 1

⇒ Students of Section 2 are more consistent.

Also,

mean of Section 2 > mean of Section 1,

⇒average score of Section 2 student > Average score of Section 1 student.

∴ we get

Section 2 did better overall on the exam.