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Measures of Central Tendency Mean, Median, Mode, Range Curriculum Objective: The students will determine the mean, median, mode and range of a specific set of data and apply these tendencies to solving problems. Map Tap 2003-2004 Measures of Central Tendency 2 Mean Data:100, 78, 65, 43, 94, 58 Mean: The sum of a collection of data divided by the number of data 43+58+65+78+94+100=438 438÷6=73 Mean is 73 Map Tap 2003-2004 Measures of Central Tendency 3 Median Data:100, 78, 65, 43, 94, 58 Median: The middle number of the set of data. If the data has an even number of data, you add the 2 middle numbers and divide by 2. 65+78=143 143÷2=71.5 Median is 71.5 Map Tap 2003-2004 Measures of Central Tendency 4 Mode Data:100, 78, 65, 43, 94, 58 Mode: Number in the data that happens most often. No mode Map Tap 2003-2004 Measures of Central Tendency 5 What Does It Mean to Understand the Mean? We are learning the importance of statistical concepts. We are learning to find, use and interpret measures of central tendency. We will be learning the relationship of the mean to other measures of central tendency (mode and median) Map Tap 2003-2004 Measures of Central Tendency 6 Properties of Arithmetic Mean The following properties Will be useful in understanding The arithmetic mean and its Relationship to the other Measures of central tendency Mode and Median These principals were identified By Strauss and Bichler Through their research in 1988 Map Tap 2003-2004 Measures of Central Tendency 7 What Does It Mean To Understand The Mean? The mean is located between the extreme values. The mean is influenced by values other than the mean. The mean does not necessarily equal one of the values that was summed. The mean can be a fraction. When you calculate the mean, a value of 0, if it appears, must be taken into account. The mean value is representative of the values that were averaged. Map Tap 2003-2004 Measures of Central Tendency 8 What Would Happen If… You are given the following set of Data: 1, 1, 2, 2, 2, 2, 3, 3, 4, 5 Map Tap 2003-2004 Measures of Central Tendency 9 1, 1, 2, 2, 2, 2, 3, 3, 4, 5 Determine the mean and the median of the given set of numbers. Map Tap 2003-2004 Measures of Central Tendency 10 1, 1, 2, 2, 2, 2, 3, 3, 4, 5 What happens to the mean if a new number, 2 ,is added to the given data? Explain why this result occurs. Map Tap 2003-2004 Measures of Central Tendency 11 1, 1, 2, 2, 2, 2, 3, 3, 4, 5 What happens to the mean if a new number, 8, is added to the given data? Explain why this result occurs. Map Tap 2003-2004 Measures of Central Tendency 12 1, 1, 2, 2, 2, 2, 3, 3, 4, 5 What happens to the mean if a new number, 0, is added to the given data? Explain why this result occurs. Map Tap 2003-2004 Measures of Central Tendency 13 1, 1, 2, 2, 2, 2, 3, 3, 4, 5 What happens to the mean if two new numbers, 2 and 3, are added to the given data? Explain why this result occurs. Map Tap 2003-2004 Measures of Central Tendency 14 1, 1, 2, 2, 2, 2, 3, 3, 4, 5 What happens to the mean if a new number, 30, is added to the given data? How well does the mean represent the new data? Can you find another measure of central tendency that better represents the data? Map Tap 2003-2004 Measures of Central Tendency 15 The Median The median is best describes the data set when there is an outlier. Map Tap 2003-2004 Measures of Central Tendency 16 1, 1, 2, 2, 2, 2, 3, 3, 4, 5 Determine the mode of the given set of numbers. Map Tap 2003-2004 Measures of Central Tendency 17 The Mode The mode best describes the data set when comparing data or when the data includes categories Map Tap 2003-2004 Measures of Central Tendency 18