Measures of Central Tendency Mean, Median, Mode, Range Standard VII-5

Mean  Data:100, 78, 65, 43, 94, 58  Mean: The sum of a collection of data divided by the number of data = ÷6=73 Mean is 73

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=71.5 Median is 71.5

Mode  Data:100, 78, 65, 43, 94, 58  Mode: Number in the data that happens most often.  No mode

What Does It Mean to Understand the Mean?  In middle school we are learning the importance of statistical concepts.  In middle school 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)

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

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.

What Would Happen If…  You are given the following set of Data: 1, 1, 2, 2, 2, 2, 3, 3, 4, 5

 Create a realistic story to represent the data.  Examples:  Number of TV  Money  Time  Number of Pets

Determine the mean and the median of the given set of numbers. 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. 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. 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. 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. 1, 1, 2, 2, 2, 2, 3, 3, 4, 5

Find two numbers that can be added to the given data and not change the mean. Explain how you chose these two numbers. 1, 1, 2, 2, 2, 2, 3, 3, 4, 5

Find three numbers that can be added to the given data and not change the mean. Explain how you chose these three numbers. 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? 1, 1, 2, 2, 2, 2, 3, 3, 4, 5

Find two numbers that can be added to the given data that change the mean but not the median. Explain how you chose these two numbers. 1, 1, 2, 2, 2, 2, 3, 3, 4, 5