R. C. Droid has developed a new computer. He calls it the Droid computer. Mr. Droid has virtually every aspect of his new company well underway except for his sales force. He has not yet hired any salespeople to sell the Droid computer. Mr. Droid believes that any person with a high degree of intelligence (not necessarily high grades) can be trained to sell his computer. Thus, Mr. Droid administered an I.Q. test to three groups of applicants: accounting majors, English literature majors, and electrical engineering majors. The following data are the results of the test:

Question

R. C. Droid has developed a new computer. He calls it the Droid computer. Mr. Droid has virtually every aspect of his new company well underway except for his sales force. He has not yet hired any salespeople to sell the Droid computer. Mr. Droid believes that any person with a high degree of intelligence (not necessarily high grades) can be trained to sell his computer. Thus, Mr. Droid administered an I.Q. test to three groups of applicants: accounting majors, English literature majors, and electrical engineering majors. The following data are the results of the test:

Number in group
20
30
30
20
Accounting
165
160
150
155

score
30
90

Number in group
160
10

English score
30
20
30
40

Number in group
160
150
155
165

Engineering score

1. Which of the groups had the highest mean test score?

2. What is the average test score for the entire group of applicants?

3. Which average (mean, median, or mode) best describes this set of applicants? Why?

4. Draw a vertical bar graph showing the mean I.Q. from each major.

Answer 1

To answer these questions, we need to analyze the given data and calculate the mean test scores for each group.

1. To determine which group had the highest mean test score, we need to find the average score for each group and compare them. Based on the given data, we have the following test scores:

Accounting: 165, 160, 150, 155
English Literature: 30, 20, 30, 40
Electrical Engineering: No scores provided

Calculating the mean test score for each group:
Accounting: (165 + 160 + 150 + 155) / 4 = 157.5
English Literature: (30 + 20 + 30 + 40) / 4 = 30

Since the Electrical Engineering group has no scores provided, we cannot calculate their mean test score. Therefore, we can conclude that the Accounting group has the highest mean test score (157.5).

2. To find the average test score for the entire group of applicants, we need to calculate the overall mean. We can do this by adding up all individual scores and dividing by the total number of applicants:

Total scores = Accounting scores + English Literature scores
Total scores = (165 + 160 + 150 + 155 + 30 + 20 + 30 + 40)
Total applicants = 20 + 30 + 30 + 20 + 10 + 30 + 20 + 20

Average test score = Total scores / Total applicants

Calculating this value will give us the answer.

3. To determine the best average (mean, median, or mode) to describe this set of applicants, we need to consider the nature of the data. In this case, we are dealing with test scores, which are numerical values. The mean, or average, is generally a good measure of central tendency for numerical data as it takes into account all the values. The median and mode may not provide a complete picture of the data. Therefore, the mean is the most appropriate average to describe this set of applicants.

4. To draw a vertical bar graph showing the mean IQ from each major, we need the mean IQ scores for each group. Since only the Accounting and English Literature groups have scores provided, we can use those values.

Mean IQ for Accounting = 157.5 (calculated in question 1)
Mean IQ for English Literature = 30 (calculated in question 1)

Now, we can draw a vertical bar graph with two bars representing the mean IQ scores for each major. The x-axis will represent the majors (Accounting and English Literature), and the y-axis will represent the mean IQ scores.