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# Statistics Topic

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DETERMINE THE MEAN, MEDIAN, AND MODE FOR A GIVEN SET OF DATA • A set of data is a collection of numbers related to a specific topic: scores on a test, weights of objects, high temperatures of the day, students who eat particular lunches, etc. o This data can be organized and analyzed using math tools. • The mean is the numerical average of a set of numbers. It is calculated by adding all the values in a set and then dividing by the number of values. • The mode is the middle value, calculated by ordering the values and determining the value halfway between the first and last value. o The mode is the value which occurs most frequently. How to determine the mean, median, and mode for a given set of data: • To determine the mean, add the values and divide by the number of values: o Scores on a series of tests: 65, 76, 98, 84, 100, 76 o Add the values → 499 o Divide by the number of values: 499 ÷ 6 o The mean is 83.17 • To determine the median, order the values and then choose the value in the middle o Scores on a series of tests: 76, 98, 84, 100, 76 o Order: 76, 76, 84, 98, 100 o The median is the “middle” value o The median is 84 © 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.

• To determine the median of an even number of values, order the values, find the middle, and calculate the average between the two middle scores: o Scores on a series of tests: 65, 76, 98, 84, 100, 76 o Order: 65, 76, 76, 84, 98, 100 o The middle of this series is between 76 and 84 o The median is the average of 76 and 84 o Median = (76 + 84) ÷ 2 o The median is 80 • To determine the mode, look for the value which appears most frequently: o Scores on a series of tests: 65, 76, 98, 84, 100, 76 o Look for the value that occurs most frequently o 2 scores are 76, the other scores occur only once o The mode is 76 • It is possible for the mean, median, and mode to be the same value for a specific set. However, this is very unusual. Try This! What is the mean for this set? 35, 67, 23, 17, 43, 65, 81 _____________________________________ What is the mode for this set? 43, 54, 54, 23, 43, 43 _____________________________________ What is the median for this set? 13, 17, 19, 25, 29 _____________________________________ What is the median for this set? 35, 67, 23, 17, 43, 65, 81 _____________________________________ What is the median for this set? 45, 32, 51, 34, 25, 30 _____________________________________ © 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.