Finding the Mean and Median from Graphs Lesson 5.3.2

5.3.2 Finding the Mean and Median from Graphs California Standards: Lesson 5.3.2 Finding the Mean and Median from Graphs California Standards: Statistics, Data Analysis, and Probability 1.1 Compute the range, mean, median, and mode of data sets. Statistics, Data Analysis, and Probability 2.3 Analyze data displays and explain why the way in which the question was asked might have influenced the results obtained and why the way in which the results were displayed might have influenced the conclusions reached. What it means for you: You’ll see how bar graphs, line plots, and pictographs can make it easier for you to find the mean and median of data sets. Key words: data set bar graph line plot pictograph mean median

5.3.2 Finding the Mean and Median from Graphs Lesson 5.3.2 Finding the Mean and Median from Graphs In the last Lesson, you saw how to find the mode and the range of a data set from a line plot, bar graph, or pictograph. That’s not all you can do with these graphs. You can use them to find the mean and the median too.

5.3.2 Finding the Mean and Median from Graphs Lesson 5.3.2 Finding the Mean and Median from Graphs You Can Use a Graph to Find the Median The median is the middle value when a set of values is put in order. A graph can give you the information you need to find the median of a data set.

5.3.2 Finding the Mean and Median from Graphs Lesson 5.3.2 Finding the Mean and Median from Graphs Example 1 What is the median of the data set shown on this line plot? Solution Remember that each X on the line plot represents one item in the data set. So you can turn the plot back into a set of data: {9, 10, 10, 10, 10, 11, 11, 11, 13, 13} There are ten values in the set, so the median is midway between the fifth and sixth values. The fifth and sixth values are 10 and 11, so the median is 10.5. Solution follows…

5.3.2 Finding the Mean and Median from Graphs Guided Practice Lesson 5.3.2 Finding the Mean and Median from Graphs Guided Practice In Exercises 1–2, find the median of the data set shown on each graph. 1. Median of: {19, 20, 20, 20, 20, 20, 21, 21, 21, 22, 23, 23, 23} = 7th value = 21 2. Median of: {5, 5, 5, 5, 5, 7, 8, 8, 8, 9, 9, 9, 9} = 7th value = 8 Solution follows…

5.3.2 Finding the Mean and Median from Graphs Guided Practice Lesson 5.3.2 Finding the Mean and Median from Graphs Guided Practice In Exercises 3–4, find the median of the data set shown on each graph. 3. Median of: {4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7} = 9th value = 5 4. Median of: {0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7} = midway between 10th and 11th values = 3 Solution follows…

5.3.2 Finding the Mean and Median from Graphs Lesson 5.3.2 Finding the Mean and Median from Graphs You Can Use a Graph to Find the Mean The mean of a data set is the sum of all the values, divided by the number of items in the data set. There are a couple of ways that you can use a graph to find the mean of a data set.

5.3.2 Finding the Mean and Median from Graphs Lesson 5.3.2 Finding the Mean and Median from Graphs Example 2 What is the mean of the data set shown on this line plot? Solution This is the same graph as in Example 1. So the data set is: {9, 10, 10, 10, 10, 11, 11, 11, 13, 13} The mean is the sum of these values, divided by the number of values. (9 + 10 + 10 + 10 + 10 + 11 + 11 + 11 + 13 + 13) ÷ 10 = 108 ÷ 10 = 10.8 Solution follows…

5.3.2 Finding the Mean and Median from Graphs Lesson 5.3.2 Finding the Mean and Median from Graphs Example 3 What is the mean of the data set shown on this bar graph? Solution The scale tells you that there are 5 items of data with a value of 1, 8 items with a value of 2, and so on. You can turn this into a multiplication to find the sum of all the values in the data set. Solution continues… Solution follows…

5.3.2 Finding the Mean and Median from Graphs Lesson 5.3.2 Finding the Mean and Median from Graphs Example 3 What is the mean of the data set shown on this bar graph? Solution (continued) The data set has: 5 items with the value 1 5 × 1 = 5 8 items with the value 2 8 × 2 = 16 5 items with the value 3 5 × 3 = 15 9 items with the value 4 9 × 4 = 36 3 items with the value 5 3 × 5 = 15 30 87 The sum of the values is 87, and there are 30 values. So the mean is 87 ÷ 30 = 2.9.

5.3.2 Finding the Mean and Median from Graphs Guided Practice Lesson 5.3.2 Finding the Mean and Median from Graphs Guided Practice 5. Find the mean of the data set shown on each graph. A Mean = (19 + 20 + 20 + 20 + 20 + 20 + 21 + 21 + 21 + 22 + 23 + 23 + 23) ÷ 13 = 273 ÷ 13 = 21 B Mean = (5 + 5 + 5 + 5 + 5 + 7 + 8 + 8 + 8 + 9 + 9 + 9 + 9) ÷ 13 = 92 ÷ 13 = 7.08 Solution follows…

5.3.2 Finding the Mean and Median from Graphs Guided Practice Lesson 5.3.2 Finding the Mean and Median from Graphs Guided Practice 5. Find the mean of the data set shown on each graph. C Mean = (4 + 4 + 4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 5 + 5 + 6 + 6 + 7 + 7 + 7) ÷ 17 = 86 ÷ 17 = 5.06 D Mean = (0 + 0 + 0 + 1 + 1 + 2 + 2 + 2 + 2 + 2 + 4 + 5 + 5 + 5 + 5 + 6 + 6 + 6 + 7 + 7) ÷ 20 = 68 ÷ 20 = 3.4 Solution follows…

5.3.2 Finding the Mean and Median from Graphs Guided Practice Lesson In Exercise 6, find the mean of the data set shown on the graph. 6. Mean = (28 + 28 + 29 + 29 + 29 + 29 + 29 + 30 + 30 + 30 + 30 + 31 + 31 + 31 + 31 + 31 + 31 + 32) ÷ 18 = 539 ÷ 18 = 29.94 Solution follows…

5.3.2 Finding the Mean and Median from Graphs Guided Practice Lesson In Exercise 7, find the mean of the data set shown on the graph. 7. Mean = (41 + 41 + 41 + 41 + 42 + 42 + 42 + 42 + 43 + 43 + 43 + 43 + 43 + 43 + 43 + 44 + 44 + 45 + 45) ÷ 20 = 856 ÷ 20 = 42.8 Solution follows…

5.3.2 Finding the Mean and Median from Graphs Independent Practice Lesson 5.3.2 Finding the Mean and Median from Graphs Independent Practice Which of the line plots below have: 1. a median of 32.5? 2. a mean less than 12? D A and C A B C D Solution follows…

5.3.2 Finding the Mean and Median from Graphs Independent Practice Lesson 5.3.2 Finding the Mean and Median from Graphs Independent Practice All the classes in an elementary school have from 25 to 31 students. This pictograph shows the class sizes. 3. How many classes are there in this school? 13 4. Find the median and mean number of students in each class. median = 28 mean = 27.69 Solution follows…

5.3.2 Finding the Mean and Median from Graphs Independent Practice Lesson 5.3.2 Finding the Mean and Median from Graphs Independent Practice 5. Which one of the graphs below represents a data set that has the same mean, median, and mode? C A B C Solution follows…

5.3.2 Finding the Mean and Median from Graphs Round Up Lesson 5.3.2 Finding the Mean and Median from Graphs Round Up The types of graphs you’ve used to find the mean, median, mode, and range of a data set are all similar types of graphs. Bar graphs, line plots, and pictographs all show the same sort of information. There are other types of graphs that can show data in different ways. You’ll see a couple of these in the next Lesson.