ORGANIZING DATA • Organizing data refers to collecting, organizing, and interpreting data. • Data is usually mathematical information in a set of numbers. If collecting data about the ages of people living on one street, the data is all the ages. • The data can then be organized into groups, and evaluated. Mean, mode, median and range are different ways to evaluate data. o The mean is the average of the data. o The mode refers to the number that occurs the most often in the data. o The median is the middle number when the data is arranged in order from lowest to highest. o The range is the difference in numbers when the lowest number is subtracted from the highest number. • Data can be organized into a table, such as a frequency table. A frequency table displays the data in a table with one side listing the intervals of data or categories of data and the other side listing the frequency of the intervals or categories of data. o The frequency of the data can be shown with tally marks or numbers. How to use Organizing Data: • If there is a list of data given, the mean or average of the data can be found by adding the numbers together and dividing by the total number of data. • Given the data below of ages, the mean can be found as follows: Ex. 23, 35, 22, 45, 40, 22, 16, 33, 41 Added together = 277 277 ÷ 9 = a mean of 30.777 or 30.8 • If the mean is given, but one of the numbers of the data is missing, the missing number can be found. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
Example: Sue wants to have a 90 average in math. Her tests scores are 85, 92, 87, and 95. She has to take one more test. What should her score be to have a 90 average? Since Sue wants a 90 average, the total she would need is 5 · 90 or 450. So far, she has an 85, 90, 87, and 95 for a total of 357. She would need 450 - 357, or a 93 on her next test to receive a 90 average. • The median of a set of data is the middle number. Given the data below of ages, the median can be found as follows: The data 23, 35, 22, 45, 40, 22, 16, 33, 41 is first organized from low to high to become 16, 22, 22, 23, 33, 35, 40, 41, 45. The median can be found by counting the numbers, 9, and finding the middle number, the 5th one, and in this case, 33, so 33 is the median. If a set of data has an even number of data, the median can be found by averaging the two middle numbers. • The mode of the given data: 23, 35, 22, 45, 40, 22, 16, 33, 41, is 22, since it is the only number that is listed more than once. o It is possible for a set of data to have more than one mode. If a list of data has numbers that occur multiple times, then the numbers that occur the most are the mode. If all the numbers occur one time, the set of data has no mode. • The range of the data: 16, 22, 22, 23, 33, 35, 40, 41, 45, is the highest number, 45, minus the lowest number, 16, which equals 29. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
• Tables display data so it is easy to read. A frequency table is used to display intervals or categories, and how many times that interval or category is picked. o For example, if 25 students were asked what their favorite number was out of the numbers 1-6, a frequency table would display the numbers 1-6 and each number would have tally marks to show how many times that number was picked as shown below. Try This! Find the mean, mode, median and range of the following data: 2, 5, 10, 2, 6, 7, 14, 6, 2, 8, 11, 9, 3 Make a frequency table to record the following data: sharks- 8 sea turtles- 4 angel fish- 15 dolphins- 2 © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.