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: 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. How to Find the Mean The mean is just the average of the numbers. 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 Add the numbers: 6 + 11 + 7 = 24 Divide by how many numbers (ie we added 3 numbers): 24 3 = 8 Why Does This Work? The Mean is 8 It is because 6, 11 and 7 added together is the same as 3 groups of 8 if you made the stacks the same size: 3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56
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: 3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29 In order these numbers are: 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= 7) 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 (number of units) before adding up the total and dividing by the total number of units. 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 Trigonometry B 3 4 History D 1 3 P.E. A 4 1 Music Appreciation B 3 2 TOTAL: GPA:
Answers Ch. 8 Review - Analyzing Data and Graphs 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 7) Grade Points: 8,12,3,4,6, Total Unit:14, Total Grade Points: 33, GPA: 2.36
Complete. Bar Graphs 1. Number of Books Owned a. If Justin sold two-fifths of his books for $3 each, how much money would Justin get from selling the books? b. Which of the children own at least 75 books? c. What is the average number of books owned? Round your answer to the nearest whole number. 2. a. What is the average number of seeds planted? Round your answer to the nearest seed. b. What is the median of the data? c. Three-fourths of the seeds planted on Monday were watermelon seeds. How many of the seeds planted on Monday were not watermelon seeds? 3. Money Spent on Sneakers a. What is the median of the data? b. What is the average amount spent on all 7 sneakers? Round your answer to the nearest cent. c. How much did Sarah and Rachel spend altogether on their sneakers?
Answer Key 0158964 1 a. If Justin sold two-fifths of his books for $3 each, how much money would Justin get from selling the books? $102 b. Which of the children own at least 75 books? Justin, Kyle, Cameron, and Sydney c. What is the average number of books owned? Round your answer to the nearest whole number. 71 2 a. What is the average number of seeds planted? Round your answer to the nearest seed. 238 b. What is the median of the data? 250 c. Three-fourths of the seeds planted on Monday were watermelon seeds. How many of the seeds planted on Monday were not watermelon seeds? 50 seeds 3 a. What is the median of the data? $55 b. What is the average amount spent on all 7 sneakers? Round your answer to the nearest cent. $61.43 c. How much did Sarah and Rachel spend altogether on their sneakers? $165
Complete. Line Graphs 1. School Play Attendance a. What was the total attendance for all of the play performances? b. How many more people attended the performance on Wednesday than the attendance on Friday? c. Between which two days was there the greatest increase in attendance? 2. Price of BuyMe Stock a. Which day had the highest cost per share? b. On which day(s) was the price at least $14? c. Between which days did the stock price decrease by $3? 3. Attendance a. Which games(s) did not have an attendance of at least 375 people? b. Between which two games was there the greatest increase in attendance? c. Which game had the lowest attendance?
Answer Key 0694653 1 a. What was the total attendance for all of the play performances? 1525 b. How many more people attended the performance on Wednesday than the attendance on Friday? 225 c. Between which two days was there the greatest increase in attendance? from Monday to Tuesday and from Friday to Saturday 2 a. Which day had the highest cost per share? Wednesday b. On which day(s) was the price at least $14? Monday, Wednesday, and Thursday c. Between which days did the stock price decrease by $3? from Monday to Tuesday, from Wednesday to Thursday, and from Thursday to Friday 3 a. Which games(s) did not have an attendance of at least 375 people? Game #2 and Game #3 b. Between which two games was there the greatest increase in attendance? from Game #3 to Game #4 c. Which game had the lowest attendance? Game #2
Complete. Circle Graphs 1. How students get to school A Walk 20% B Bike 12% C Drive 22% D Take the bus 46% a. If the school has 69 students, how many students bike to school? b. What fraction of the students walk to school? 2. Favorite Season (% of vote) A Winter 30% B Fall 29% C Spring 15% D Summer 26% a. What is the least popular season? b. What fraction of the total votes did fall receive? 3. Number of Cars in a Family (% of families) A no cars 22% B 3 cars 19% C 4 cars 24% D 1 car 16% E 2 cars 19% a. What fraction of the families have exactly 1 car? b. If 138 families were surveyed, how many fewer families have 1 car than those that have no cars? 4. Animals at an Aquarium A Tropical Fish 50% B Dolphins 8% C Sea horses 28% D Sharks 14% a. What fraction of the animals at the aquarium are sea horses? b. The number of sharks is about how many times the number of dolphins?
Answer Key 0611543 1 a. If the school has 69 students, how many students bike to school? 8 b. What fraction of the students walk to school? 1 5 2 a. What is the least popular season? Spring b. What fraction of the total votes did fall receive? 29 100 3 a. What fraction of the families have exactly 1 car? 4 25 b. If 138 families were surveyed, how many fewer families have 1 car than those that have no cars? 6 4 a. What fraction of the animals at the aquarium are sea horses? 7 25 b. The number of sharks is about how many times the number of dolphins? 1.75
Histograms 25 people were surveyed about their favorite girl scout cookies. Below is a frequency table and some charts to fill out. Fill in the percentages in the below and in each slice of the pie chart. Also, make a column chart, or Histogram, illustrating the results. Favorite Girl Scout Cookie Thin Mints 6 Caramel Delights 4 Peanutbutter Patties 4 Lemon Chalet Cremes 3 Shortbread Trefoils 3 Do-Si-Do's 2 Thank U Berry Much 2 Dulce de Leche 1 Total 25 Percentage 1) What was the most popular cookie? 2) What was the least popular cookie? 3) What where the third most popular cookies? 4) How many more people surveyed chose Thin Mints than Shortbread Trefoils?