1. Section 3.1 Measures of Central Tendency: Mode, Median, and Mean

2. 2 Usually, one number is used to describe the entire sample or population – the average. three of the major ways to measure center of data: 1.Mode 2.Median 3.Mean

3. 3 Mode -Data value that occurs the most -Not every data set has a mode (Ex: professor assigns equal # of A’s, B’s, C’s, D’s, F’s) -Mode is not stable -Think tallest bar on a histogram -Most in a class (ex: bimodal means 2 modes) - Relevant in cases like most frequently requested shoe size

4. 4 -Order data from smallest to largest -50% of the data below and 50% above the median Ex: Data on price per ounce in cents of chips: 19 19 27 28 18 35 a) Mode? b) Median? c) Average? d) What if you add 80 to the data set? Median

5. 5 If we take out 35 from the data. Median = 19 e) Is $10.45 reasonable to serve an ounce of chips to 55 people? Yes, the median price of the chips is 19 cents per ounce.

6. 6 NOTE #1: The median uses the position - extreme values usually does not change it much. Ex: the median is often used as the average for house prices. NOTE #2: Extreme values inflate or deflate the average (mean)

7. 7 Mean

8. 8 A resistant measure is one that is not influenced by extremely high or low data values. ***The mean is not a resistant measure of center ***The median is more resistant measure of center

9. 9 Trimmed Mean ***More resistant than the regular mean -- trim the lowest 5% of the data and highest 5% of the data (works the same for a 10% trimmed mean) Procedure: 1.Order data 2.Multiply 5% by n and round to the nearest integer 3.that value is how many data points you trim from each end 4.Take the average of the remaining values

10. 10 Measures of Central Tendency: Mode, Median, and Mean Symmetrical data: mean, median, and mode are the same or almost the same. Left-Skewed data: mean < median and median < mode Right-Skewed data: mean > median and Median > mode

11. 11 Relationship: Mode, Median, and Mean Figure, shows the general relationships among the mean, median, and mode for different types of distributions. (a)Mound-shaped symmetrical (b) Skewed left (c) Skewed right

12. 12 Weighted Mean Suppose your midterm test score is 83 and your final exam score is 95. Using weights of 40% for the midterm and 60% for the final exam, compute the weighted average of your scores.

13. 13 Solution

14. 14 Harmonic Mean

15. 15 Geometric Mean

16. 16 Example 1 – In the calculator Belleview College must make a report to the budget committee about the average credit hour load a full-time students carries. (A 12-credit-hour load is minimum requirement for full-time status. For the same tuition, students may take up to 20 credit hours.) A random sample of 40 students yielded the following information (in credit hours): 17 121712181912 12141515121314 15141616201315 18161712121715 121513182012 171614191312

17. 17 Example 2 Barron’s Profiles of American Colleges, 19 th edition, lists average class size for introductory lecture courses at each of the profiled institutions. A sample of 20 colleges and universities in California showed class sizes for introductory lecture courses to be: 142020202023253030 30353535404042505080

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