Central Tendency, Mean, Median, Standard Deviation

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Colorado Technical University *

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502

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Statistics

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Apr 3, 2024

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docx

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Uploaded by MajorWaterFinch27

Introduction If you randomly asked people what they knew about statistics, the terms mean , median , and mode would probably be a common answer. In statistics, these terms are most commonly used to measure the central tendency of a data set. Learning Material Central tendency is the measurement around where all the data are clustered. There are several ways to measure central tendency, but the most common are the mean and median. The mean or average is calculated as the sum of all data values in a set divided by the total number of data values in the set. One common use of averages for students is course grades: where x represents in the individual data values and n is the number of data values. The median is calculated in a different manner from the mean. For the median, the data values have to be sorted from lowest value to highest value. The median represents the actual middle value in the list. If the data set contains an odd number of values, the median is the middle value in the list. If the data set contains an even number of values, the median is the mean or average of the two middle values. The mean and median both accurately display the central value of the data. The mean is more commonly used, but the median can be more effective if there is a value or two significantly more or less than all the others in the data set, or in other words, if the data set contains extreme values. Extreme values in a data set are outliers. When a data set does not have an outlier, the mean and median may be the same value or close values. The mode displays the values in the data set that appear the most frequently. The mode in a bar graph would have the highest column. Because students can relate to average grades in classes, examine a problem. The data set are the test scores for the class for a particular test. The instructor examines the effectiveness of the lesson based on the scores. Data set: 80, 70, 83, 90, 75, 96, 82, 100, 45 Nine test scores provide the value of 9 for n in the mean formula:

The mean or average score for the class was an 80. To calculate the median, the values have to be ordered, as follows: Ordered list = 45, 70, 75, 80, 82, 83, 90, 96, 100 With an odd number of values, the median is the middle of the list. For nine values, the middle is the fifth value. Therefore, the median is 82. Because none of the values repeat, there is not a mode for this data set. The mean and median for the scores are close, but the median is more accurate with the outlier score of 45. Summary The mean, median, and mode represent the central or most common values in a data set. The central tendency indicates the values in the data set around the cluster. The central tendency values will be close unless the data include an outlier. Interactive Example For the given data set, which is more effective, the mean or the median? Median because it is the center value of the list Which of the following is not a measure of central tendency? Range Salaries (in $1,000 increments): 50, 60, 55, 61, 59, 52, 59, 59 Question 3 Given the salaries in $1,000s, the average salary is $56,875 , and the most common salary is $59,000 . Your department has the following sales totals in $1,000 increments: 33, 31, 34, 29, 40. Question 4 Given the following sale totals for your department, the mean is $33,400 , and the median is $33,000 . You have to include the central tendencies in your report. To take it more positive, you can report the Mean .

You have been given the following data set: 13, 12, 11, 13, 14, 12, 13, 14, 13, 12. Question 5 For the given data set, find the mode. 13 You have determined the data set representing the number of missed deadlines for the year: 1, 2, 1, 4, 1, 1, 1, 2, 1, 2, 1, 1. Question 1 Would you report the mean or median to your manager for the following data? Median due to the outlier of 4 You have been provided the following data set: 3, 5, 4, 7, 2, 5, 5, 4, 1. Question 5 For the given data set, the mean is 4 , the median is 4 , and the mode is 5 . You have been given the following data set: 90, 92, 90, 91, 92, 90, 93, 94. Question 6 For the given data set, the mean is 91.5 , the median is 91.5 , and the mode is 90 . The median is more accurate than the mean when a data set contains which of the following? Outliers

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