How to find the Median Value It's the middle number in a sorted list. To find the Median, place the numbers you are given in value order and find the middle number. Look at these numbers: 3, 13, 7, 5, 21, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29 If we put those numbers in order we have: 3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56 There are fifteen numbers. Our middle number will be the eighth number: 3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56 The median value of this set of numbers is 23. (Note that it didn't matter if we had some numbers the same in the list) BUT, if there are an even amount of numbers things are slightly different. In that case we need to find the middle pair of numbers, and then find the the value that would be half way between them. This is easily done by adding them together and dividing by two. An example will help: 3, 13, 7, 5, 21, 23, 23, 40, 23, 14, 12, 56, 23, 29 If we put those numbers in order we have: 3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56 There are now fourteen numbers and so we don't have just one middle number, we have a pair of middle numbers: 3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56 In this example the middle numbers are 21 and 23. To find the value half-way between them, add them together and divide by 2: 21 + 23 = 44 44 2 = 22 And, so, the Median in this example is 22.
The mean is just the average of the numbers. Ch. 9.1-9.2 Analyzing Data and Graphs How to Find the Mean It is easy to calculate: Just add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count. Example 1: What is the Mean of these numbers? 6, 11, 7 Why Does This Work? Add the numbers: 6 + 11 + 7 = 24 Divide by how many numbers (ie we added 3 numbers): 24 3 = 8 The Mean is 8 It is because 6, 11 and 7 added together is the same as 3 lots of 8: It is like you are "flattening out" the numbers EXAMPLE: Find the missing number, n: 11, 17, n, 7, and 8 mean = 12 In this case we know the mean, but one of the numbers is missing. How do we calculate the mean? We add up each of the numbers, then divide the sum by how many numbers there are. How many numbers are there? 5. (11 17 n 7 8) 5 12 How do we solve for n? Multiply both sides by 5 so we can cancel out the 5 on the left. (11 17 n 7 8) (5) 12(5) 5 11 + 17 + n + 7 + 8 = 60 Now add everything you can to simplify this equation. 43 + n = 60 Now all you have to do is subtract both sides by 43 to isolate n. 43 43 + n = 60 43 n = 17 Check: Is 12 the mean of 11, 17, 17, 7, and 8? (11 + 17 + 17 + 7 + 8)/5 = 60/5 = 12 Yes.
How to Find the Mode or Modal Value The mode is simply the number which appears most often. To find the mode or modal value requires you to put the numbers you are given in order. Look at these numbers: In order these numbers are: 3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29 3, 5, 7, 12, 13, 14, 20, 23, 23, 23, 23, 29, 39, 40, 56 This makes it easy to see which numbers appear the most. In this case the mode or modal value is 23. Range (statistics) The difference between the lowest and highest values. In the set of numbers {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the range is 9-3 equals 6.
Find the range for each set of data. 1. 23, 23, 25, 4, and 15 range: 2. 2, 5, 17, 21, 2, 2, and 7 range: Find the mean, median, and mode of each set of data. 3. 3, 29, 16, 3, and 29 mean: median: mode: Find the missing number, n, in each data set. 5. 8, n, 8, 8, 9, and 12 mean = 11 4. 18, 27, 3, 22, 23, and 3 mean: median: mode: 6. n, 29, 6, 6, and 7 mean = 10 n= n= Weighted Average A weighted average is one in which different data in the data set are given different "weights." For example your GPA is calculated by different weights for classes with different units. Getting an A in a 1 unit P.E. class does not carry the same weight as an A in a 4 unit math class. To calculate the weighted average, multiply each item by its weight before adding up the total and dividing by the number of items. In the table below, assign each grade a point value: A=4, B=3, C=2, D=1,F=0. Then calculate the GPA. Course Grade Point Value Units Grade Points ( Points X Units) Chemistry C 2 4 8 Trigonometry B 3 4 12 History D 1 3 3 P.E. A 4 1 4 Music Appreciation B 3 2 6 TOTAL: 33 Answers 1 21 2 19 3 mean=16; median=16; mode=3, 29 4 mean=16; median=20; mode=3 5 n = 21 6 n = 2 GPA: 2.36
Bar Graphs Ch. 9.1-9.2 Analyzing Data and Graphs a. What is the average number of seeds planted? Round your answer to the nearest seed. b. What is the median and range of the data? Median = Range = c. Three-fourths of the seeds planted on Monday were watermelon seeds. How many of the seeds planted on Monday were not watermelon seeds? Above each column of weekly earnings, write the annual earnings. What is the median annual salary for someone with a bachelor s degree? What is the median annual salary for someone with an associate degree? Assuming a constant salary over 10 years, how much more would someone with a bachelor s degree earn than someone with an associate degree? Out of 50 people, how many with only a high-school diploma are likely to be unemployed? Out of 50 people, how many with a bachelor s degree are likely to be unemployed?
Complete. Line Graphs Complete. Circle Graphs