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Lesson 5.3.1

Analyzing Graphs. Lesson 5.3.1. Lesson 5.3.1. Analyzing 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

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Lesson 5.3.1

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  1. Analyzing Graphs Lesson 5.3.1

  2. Lesson 5.3.1 Analyzing 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 meet some useful types of graphs. You’ll see how to take information from those graphs, including finding the mode and range of the data set shown. • Key words: • data set • frequency table • bar graph • line plot • pictograph • mode • range

  3. Lesson 5.3.1 Analyzing Graphs When you have lots of data in a long list, it’s not always easy to figure out what it means. That’s why it’s often converted into a graph or chart. These can show you what the spread of the data is like, and which value is most common.

  4. The total numberof students who gave each answer is added up when the survey is complete. This total is the frequency. As each student is questioned, one tally markis added in the row that matches their answer. Lesson 5.3.1 Analyzing Graphs Data Can Be Recorded on a Frequency Table Frequencyis the number of times something happens. A frequency tableis a way to record and organize data. This frequency table shows the results of a survey. A group of students was asked how many movies they each saw last month.

  5. The height of the bar labeled “None” is 2. So2studentssaw no movies last month. Lesson 5.3.1 Analyzing Graphs You can use graphsand chartsto show frequency data. On a bar graph, each bar has a labelwhich tells you what group that bar represents. The sizeof a bar tells you how largethat group is. The scaleshows that the heightof the bars represents the number of students.

  6. Lesson 5.3.1 Analyzing Graphs A line plotuses crossesmarked above a number lineto represent the data. For any number on the number line, each X above it represents one studentin the survey who saw that number of movies. 5 studentssaw four movies, so there are 5 Xs above four on the line plot.

  7. Only 1 student saw three movies. One half-symbolis used to show 1 student in that row. Lesson 5.3.1 Analyzing Graphs A pictographuses pictures or symbolsto show the data. On a pictograph, each symbol often has a value of more than one unit. You need to look at the keybefore you can read the graph. Each symbol on this pictograph represents 2 students.

  8. Lesson 5.3.1 Analyzing Graphs Guided Practice This line plot shows the number of goals scored in the soccer matches played by a school team this year. 1. In how many matches did the team score 0 goals? 3 2. In how many matches did the team score 2 or more goals? 4 3. How many matches did the team play this year? 12 Solution follows…

  9. Lesson 5.3.1 Analyzing Graphs Guided Practice This pictograph shows the number of pumpkins sold by a grocery store during five days in November. 4. When were the most pumpkins sold? Friday 5. How many pumpkins were sold on Wednesday? 15 6. On which day were exactly 30 pumpkins sold? Thursday Solution follows…

  10. Lesson 5.3.1 Analyzing Graphs Guided Practice In a survey, some students were asked which of six colors they like best. This bar graph shows the results. 7. Which color was the favorite of 3 students? Green 8. Which two colors were the least popular? Orange and yellow 9. How many students said their favorite color was either red, yellow, or blue? 14 Solution follows…

  11. Lesson 5.3.1 Analyzing Graphs A Graph Can Tell You the Range and Mode The modeof a data set is the value that occurs most often. So if a data set is made into a line plot, bar graph, or pictograph, the mode is the value with the most crosses, the biggest bar, or the most symbols.

  12. Lesson 5.3.1 Analyzing Graphs Example 1 What is the mode of the data set shown on this line plot? Solution The mode is the valueon the line plot that has the greatest number of Xsabove it. The number 19 has the most Xs above it. So the mode is 19. Solution follows…

  13. Lesson 5.3.1 Analyzing Graphs The rangeof a data set is the differencebetween the greatestand leastvaluesin the set. So it’s easier to find the range from a graph than from the raw data set because you can clearly see the least and greatest values.

  14. Example 2 Lesson 5.3.1 Analyzing Graphs What is the range of the data set shown on this bar graph? Solution The different values in the data set are the labelson the bars of the graph. So the least value in the data set is 25, and the greatest is 31. 31 – 25 = 6, so the range = 6. Solution follows…

  15. Lesson 5.3.1 Analyzing Graphs Guided Practice This pictograph shows the ages of the cars parked in a parking lot, to the nearest year. 10. What is the mode of the ages of the cars? 7 years 11. Find the range of the ages of the cars. 10 years Solution follows…

  16. Lesson 5.3.1 Analyzing Graphs Guided Practice The graph below shows the points out of 20 that the students in one class scored on a math quiz. 12. What was the mode for the quiz scores? 14 13. What is the range of quiz scores? 14 Solution follows…

  17. Lesson 5.3.1 Analyzing Graphs Independent Practice A number of dog owners were asked how many times they had taken their dog to the veterinarian in the past month.The results are shown on the pictograph below. 1. How many dog owners took their dog to the vet exactly once? 5 owners 2. How many dog owners were interviewed in total? 20 owners 3. What is the mode of the data? 0 visits 4. What is the range? 3 visits Solution follows…

  18. Lesson 5.3.1 Analyzing Graphs Independent Practice The bar graph below shows the number of lunches sold each day by a restaurant. 5. Find the mode of the data. 30 lunches 6. Find the range of the data. Number of days 6 lunches 7. For how many days was this data collected? Number of lunches sold 17 days Solution follows…

  19. Lesson 5.3.1 Analyzing Graphs Independent Practice Which of the line plots below have: 8. a range of 8? 9. a mode of 2? B A and C A B C D Solution follows…

  20. Lesson 5.3.1 Analyzing Graphs Independent Practice 10. Explain the advantages of looking at data on a line plot instead of in a data set. In a line plot, the data values are already arranged in order, so finding the median and the range has one less step involved. The Xs make it easy to visually see the mode in a quick glance and also compare the number of times each data value occurs. Solution follows…

  21. Lesson 5.3.1 Analyzing Graphs Round Up You should be able to see how useful these graphs can be. They make it much easier to spot the mode and find the range of a data set. Not only that, they organize the data. As you’ll see in the next Lesson, that can help you to find the mean and the median of the data set too.

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