statistics exam

The Weighted Mean and Working with Grouped Data

Statistics (exercises)

Aleksandra Pawłowska

Jun 9, 2020

Glossary

Weighted mean The mean obtained by assigning each observation a weight that reflects its importance. Grouped data Data available in class intervals as summarized by a frequency distribution. Individual values of the original data are not available.

Aleksandra Pawłowska The Weighted Mean and Working with Grouped Data

Task 1

Consider the following data and corresponding weights.

1 Compute the weighted mean. 2 Compute the sample mean of the four data values without

weighting. Note the difference in the results provided by the two computations.

Aleksandra Pawłowska The Weighted Mean and Working with Grouped Data

Task 1 – solution

1 Compute the weighted mean. 3.69 2 Compute the sample mean of the four data values without

weighting. Note the difference in the results provided by the two computations. 3.175

Aleksandra Pawłowska The Weighted Mean and Working with Grouped Data

Task 2

Consider the sample data in the following frequency distribution.

1 Compute the sample mean. 2 Compute the sample variance and sample standard deviation.

Aleksandra Pawłowska The Weighted Mean and Working with Grouped Data

Task 2 – solution

1 Compute the sample mean. 13 2 Compute the sample variance and sample standard deviation.

s2 = 25, s = 5

Aleksandra Pawłowska The Weighted Mean and Working with Grouped Data

Task 3

The grade point average for college students is based on a weighted mean computation. For most colleges, the grades are given the following data values: A (4), B (3), C (2), D (1), and F (0). After 60 credit hours of course work, a student at State University earned 9 credit hours of A, 15 credit hours of B, 33 credit hours of C, and 3 credit hours of D.

1 Compute the student’s grade point average. 2 Students at State University must maintain a 2.5 grade point

average for their first 60 credit hours of course work in order to be admitted to the business college. Will this student be admitted?

Aleksandra Pawłowska The Weighted Mean and Working with Grouped Data

Task 3 – solution

1 Compute the student’s grade point average. 2.5 2 Students at State University must maintain a 2.5 grade point

average for their first 60 credit hours of course work in order to be admitted to the business college. Will this student be admitted? Yes, they will

Aleksandra Pawłowska The Weighted Mean and Working with Grouped Data

Task 4

Morningstar tracks the total return for a large number of mutual funds. The following table shows the total return and the number of funds for four categories of mutual funds (Morningstar Funds500, 2008).

1 Using the number of funds as weights, compute the weighted average total return for the mutual funds covered by Morningstar.

2 Suppose you had invested $10,000 in mutual funds at the beginning of 2007 and diversified the investment by placing $2000 in Domestic Equity funds, $4000 in International Equity funds, $3000 in Specialty Stock funds, and $1000 in Hybrid funds. What is the expected return on the portfolio?

Aleksandra Pawłowska The Weighted Mean and Working with Grouped Data

Task 4 – solution

1 Using the number of funds as weights, compute the weighted average total return for the mutual funds covered by Morningstar. 7.83

2 Suppose you had invested $10,000 in mutual funds at the beginning of 2007 and diversified the investment by placing $2000 in Domestic Equity funds, $4000 in International Equity funds, $3000 in Specialty Stock funds, and $1000 in Hybrid funds. What is the expected return on the portfolio? 12.27

Aleksandra Pawłowska The Weighted Mean and Working with Grouped Data

Task 5

Based on a survey of 425 master’s programs in business administration, the U. S. News & World Report ranked the Indiana University Kelley Business School as the 20th best business program in the country (America’s Best Graduate Schools, 2009). The ranking was based in part on surveys of business school deans and corporate recruiters. Each survey respondent was asked to rate the overall academic quality of the master’s program on a scale from 1 „marginal” to 5 „outstanding”. Use the sample of responses shown below to compute the weighted mean score for the business school deans and the corporate recruiters. Discuss.

Aleksandra Pawłowska The Weighted Mean and Working with Grouped Data

Task 5 – solution

x̄deans = 3.8, x̄recruiters = 3.7.

Aleksandra Pawłowska The Weighted Mean and Working with Grouped Data