WP.2.2: WEIGHTED MEANS

[WP.2.2]

Weighted means are very common in a number of business situations.  Functional areas of business, especially accounting and finance use weighted means on a regular basis.  These measures are very straightforward but can become complex when a large number of factors are used.

I. WEIGHTED MEANS

The weighted mean equation can be mathematically summarized as follows:

[File Attached]

Statistical formula for weighted means.

Note: The “Sum Product” function in many spreadsheet programs is utilized on a regular basis to calculate weighted means.

Demonstration 1: A local manufacturing company has three work classifications for it’s hourly employees.  There are 50 workers that make $14.50 per hour, 20 that make $18.50 per hour, and 3 at $26.50 per hour.  What is the weighted average paid to the hourly employees?

Answer: $16.09

[Note: Difference from simple average]

Problem 1:  An investor purchased 100 shares of Apple (AAPL) at $106 per share, 50 shares of Alphabet (GOOG) at $750 per share, and 100 shares of Tesla Motors/SolarCity (TSLA) for $225.  What is the weighted Mean price per share?

Problem 2:  The following table describes the ages of a sample of 150 viewers of a particular children’s television show.  Find the weighted mean age of these viewers.

Problem 3:  The following table describes the number of phone calls received by GRCC’s Financial Aid office between 8:00am and 9:00am on a daily basis.  This information was collected over a time period of one year.  Find the weighted mean for the number phone calls received.

Problem 4:  A bag of “The Other Side of the Fence” grass seed advertises that, on the average, its seeds will germinate within 3 days.  A sample of 500 seeds reveals that 230 seeds germinated in 4 days, 170 seeds within 5 days, 85 seeds within 6 days, 10 seeds within 7 days, and 5 seeds within 8 days.  Find the weighted mean time for these seeds to germinate.

Problem 5:  A study of students enrolled in a particular section of BA254 this semester reveals that 30% are taking 3 credit hours, 5% are taking 6 credit hours, 40% are taking 12 credit hours, 20% are taking 15 credit hours, and 5% are taking 18 credit hours.  Find the weighted mean number of credit hours for this section of students.

Problem 6: Jerome is a full time student at GRCC. The chart below shows the grades he received for the classes he took last semester:

Calculate Jerome’s weighted average GPA for last semester

Problem 7: Alix has collected the following information from consumer surveys related to the number of miles a Mazda 6 can drive before its engine fails:

Calculate the weighted average number of miles it takes for the engine of a Mazda 6 to fail. Round to the nearest mile.

Problem 8: Students in the Principles of Accounting 1 class during the winter semester were asked to rate the difficulty of their first exam on a scale of 1 to 5 with 5 being the most difficult. 300 students were surveyed with 10% rating the difficulty as 1, 19% as a 2, 27% as a 3, 32% as a 4, and 12% as a 5. Calculate the weighted average difficulty rating for the students surveyed.

Problem 9: Luke likes to bike to school in order to avoid the rush hour traffic and the congested parking ramps. Over the past semester, he biked to school 100 times and recorded how long it took him in the table below:

Calculate the weighted average time it took for Luke to bike to school last semester.

Answers:

Problem 1: $282.40

Problem 2:  4.98 years

Problem 3:  1.94 phone calls

Problem 4:  4.78 days

Problem 5:  9.9 credit hours

Problem 6: 3.17 GPA

Problem 7: 222,822 miles

Problem 8: 3.17 difficulty rating

Problem 9: 20.08 minutes (20 minutes and 5 seconds)