Mean, Median, Mode, Range
Objective: Identify the mean, median, mode, and range in application problems
Directions: Watch the following video. Then read the lesson and take notes before completing the lesson review.
Introduction
The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list. This is what is most often meant by an average. The median is the middle value in a list ordered from smallest to largest. The mode is the most frequently occurring value on the list. Mean, median, and mode are measures of central tendency and are three different ways of expressing averages of a set of data.
Mean: The "Mean" is computed by adding all of the numbers in the data together and dividing by the number of elements contained in the data set. The mean is also called the average.
Example:
Data Set = 2, 5, 9, 3, 5, 4, 7
Number of Elements in Data Set = 7
Mean = ( 2 + 5 + 9 + 7 + 5 + 4 + 3 ) / 7 = 5
Median: The "Median" of a data set is dependent on whether the number of elements in the data set is odd or even. First, reorder the data set from the smallest to the largest then if the number of elements is odd, then the Median is the element in the middle of the data set. If the number of elements is even, then the Median is the average of the two middle terms.
Example: Odd Number of Elements
Data Set = 2,5,9,3,5,4,7
Reordered = 2,3,4,5,5,7,9
Median = 5
Example: Even Number of Elements
Data Set = 2,5,9,3,4
Reordered = 2,3,4,5,9
Median = (4+5)/2 = 4/5
Mode: The "Mode" for a data set is the element that occurs the most often. It is not uncommon for a data set to have more than one mode. This happens when two or more elements occur with equal frequency in the data set. A data set with two modes is called bimodal. A data set with three modes is called trimodal.
Example: Single Mode
Data Set = 2,5,9,3,5,4,7
Mode = 5
Example: Bimodal
Data Set = 2,5,2,3,5,4,7
Modes = 2 and 5
Example: Trimodal
Data Set = 2, 5, 2, 7, 5, 4, 7
Modes = 2, 5, and 7
Range: The "Range" for a data set is the difference between the largest value and smallest value contained in the data set. First, reorder the data set from smallest to largest then subtract the first element from the last element.
Example:
Data Set = 2, 5, 9, 3, 5, 4, 7
Reordered = 2, 3, 4, 5, 5, 7, 9
Range = (9-2) = 7
Lesson Review
Directions: Calculate the mean, median, mode & range for the following data sets.
1) 61, 98, 60, 57, 81, 93
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2) 72, 18, 78, 94, 73
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3) 73, 66, 80, 81, 45
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4) 72, 31, 80, 97, 65
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5) 13, 85, 50, 79, 83
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6) 35, 74, 76, 93, 84, 22
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7) 72, 55, 11, 55, 42, 25, 79, 69
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8) 93, 15, 11, 58, 94, 87, 73, 16, 21
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9) 17, 45, 12, 74, 89, 57
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10) 52, 35, 55, 23, 30
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