Measures of central tendency (ungrouped data)

1. Measures of Central Tendency (Ungrouped Data) Prepared by: Lenny M. Sanchez Lilianne D. Soriano BSEd Math III

2. Objectives: I can define mean, median and mode. I can find the mean, median and mode of the given set of data. I can describe the data in terms of the mean, median and mode.

3. Measures of Central Tendency - is simply an average or typical value in a set of scores.

4. Three Measures of Central Tendency 1. Mean - is the most commonly used measure of central tendency. It is used to describe a set of data where the measures cluster or concentrate at a point.

5. Formula: in which = mean  x = sum of all scores N , n = number of scores  

6. Example: 80 , 80, 83, 84, 85 = = 82.4

7. 2. Median represented by Md - is the midpoint of the array. The median will be either a specific value or will fall between two values . Example: The math grades of ten students are 85, 80, 88, 83, 87, 89, 84, 80, 94 and 90.

8. Arrange first the data in increasing order that is from least to greatest or vice- versa . 80, 80, 83, 84, 85, 87, 88, 89, 90, 94 Md = Md = 86

9. 3. M ode - referred to as the most frequently occurring value in a given set of data. Example: The sizes of 15 classes selected at random are : 40, 42 , 48, 46 , 42, 49, 43, 42, 38 , 42 The mode is 42 because it is the measure that occurs the most number of times.

10. Evaluation: Test I. Find the mean, median and mode of the following set of data . The data below show the score of 20 students in a Math quiz. 25 33 35 45 34 26 29 35 38 40 45 38 28 29 25 39 32 27 47 45  

11. Test II. The data below show the score of 40 students in the 2012 Division Achievement Test (DAT). Analyze the given data and answer the question. 35 16 28 43 21 17 15 16 20 18 25 22 33 18 32 38 23 32 18 25 35 18 20 22 36 22 20 14 39 22 38

12. a. What score is typical to the group of students? b. What score appears to be the median? How many students fail below that score? c. Which score frequently appears? d. Find the mean, median and mode. e. Describe the data in terms of the mean, median and mode.

13. Reference: Mathematics, Learner’s Module, pp. 491-496