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

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 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 -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: a) Mode? b) Median? c) Average? d) What if you add 80 to the data set? Median

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 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 Mean

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 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 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 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 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 Solution

14 Harmonic Mean

15 Geometric Mean

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 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:

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