Chapter 4: Probability & Statistics Section 4.4: Averages Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Mean, Median & Mode The term “average” is a general term, and can be calculated different ways. A few of the most common averages are the mean, the median, and the mode. The mean is commonly known as the "average," and this is what we get when we "add them all up and divide by how many there are." The median is the middle number in the data. The data values must be arranged in order before you can find the median. The mode is the single data value that occurs most often within the data. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Mean, Median & Mode Example: Find the mean, median and mode of the exam scores listed below. Round your answers to the nearest tenth. 91, 94, 54, 74, 59, 84, 79, 79, 80, 89, 68 Mean: (91+94+54+74+59+84+79+79+80+89+68)/11 = 77.4 Median: 54, 59, 68, 74, 79, 79, 80, 84, 89, 91, 94  79 Mode: Since there are more 79s than the other scores, the mode is 79. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Mean, Median & Mode When looking for the median, is there are an odd number of data values, the median is the one in the middle of the ordered list. If there are an even number of data values, the median is the mean of the two in the middle. Example: Find the median and mean of the following numbers. 34, 45, 56, 23, 45, 23, 34, 5438 In order, we have: 23, 23, 34, 34, 45, 45, 56, 5438 The median is (34+45)/2 = 79/2 = 39.5 Mean: (34+45+56+23+45+23+34+5438)/8 = 5698/8 = 712.25 Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Frequency Tables A frequency table is a way to arrange all of the data values from a given situation into chart form. The first column will identify the item. The second column will indicate the frequency of the item. The third column, if it exists, will indicate the relative frequency, which is just the percent that the item occurs. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Frequency Tables Example: A car dealer has 5 red cars, 6 blue cars, 3 white cars and 11 black cars. Make a relative frequency table that describes these cars. Start with a table framework that has three columns. The the first column is for the car colors. The second column is the number of cars for each color – which is the frequency. The last column is the relative frequency, which is simply the corresponding percent for each color. Color # Frequency Red 5 20% Blue 6 24% White 3 12% Black 11 44% Color # Red 5 Blue 6 White 3 Black 11 Color Red Blue White Black Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Frequency Tables Example: The given table represents the salaries at Joe’s Garage. Find the mean and median salary. Round to the nearest dollar. Mean: 5 $30,000 +6 $40,000 +2 $50,000 +1($100,000) 14 Mean = $42,143 Median: If we ranked the 14 salaries, the mean of the salaries in the 7th and 8th positions would be the median. There are five at $30,000. The 7th and 8th are both $40,000. If Joe wanted to attract a new employee, which “average” salary would he state? Why? Salary # of People $30,000 5 $40,000 6 $50,000 2 $100,000 1 Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Grade Point Averages A student’s Grade Point Average (GPA) is the measure of the student’s performance in relation to the number of credits completed. To compute it, convert the grade to its numeric equivalent and multiply by the number of credits for the corresponding course. Add together the grade points for each course, and then divide by the total number of credits and round to the hundredth or thousandth, as directed. COMMON MISTAKE A common mistake is to find the average grade instead of the average of the grade points. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Grade Point Averages Example: A student gets an A in a 3-cr math class, a C+ in a 4-cr English class, and a B- in a 3-cr history class. What is her GPA for that semester? Round to the nearest hundredth. GPA = 4.0 3 + 2.3 4 +(2.7)(3) 10 GPA = 29.3 10 = 2.93 Grade Value A 4.0 A- 3.7 B+ 3.3 B 3.0 B- 2.7 C+ 2.3 C 2.0 C- 1.7 D+ 1.3 D 1.0 D- 0.7 F 0.0 Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates