Mean-median-mode-of-grouped-data-Lyssa-Grageda.pptx

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1. Mean, median, mode of grouped data LYSSA G. GRAGEDA MR. HERNALDO OCAṄA Reporter Professor

2. Grouped data is data that has been organized into groups known as classes. It is often used in statistical analysis to simplify data and focus on key trends and patterns.

3. Suppose we want to compare the age of students in two schools and determine which school has more aged students. If we compare on the basis of individual students, we cannot conclude anything. However, if for the given data, we get a representative value that signifies the characteristics of the data, the comparison becomes easy.

4. A certain value representative of the whole data and signifying its characteristics is called an average of the data.

5. Three types of averages are useful for analyzing data. They are: Mean Median Mode

6. Mean The mean (or average) of observations is the sum of the values of all the observations divided by the total number of observations .

7. How to get the mean? To calculate the mean of grouped data, multiply the midpoints of each class by their respective frequencies, sum these products, and then divide by the total number of data points.

8. FORMULA

9. Example: AGE f ( frequency ) x ( add the class interval divided by 2) fx 11-20 3 15.5 46.5 21-30 4 25.5 102.0 31-40 7 35.5 248.5 41-50 8 45.5 364.0 51-60 5 55.5 277.5 61-70 2 65.5 131 71-80 1 75.5 75.5 ∑ 30 1 245

10. Median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger. To find the median: Arrange the data points from smallest to largest. If the number of data points is odd, the median is the middle data point in the list.

11. FORMULA lcb = lower class boundary m-median class ∑ f =summation of frequency cf - cumulative frequency bmc -before median class f- frequency w-width/class size

12. Example: AGE f ( frequency ) Lcb Add lower and upper class interval divided by 2) cf 11-20 3 10.5 3 21-30 4 20.5 7 31-40 7 30.5 14 41-50 8 40.5 22 51-60 5 50.5 27 61-70 2 60.5 29 71-80 1 70.5 30 ∑ 30

13. ∑f= 30 divided by 2= 15 ( greater than 15 is 22)

14. AGE f ( frequency ) Lcb Add lower and upper class interval divided by 2) cf 11-20 3 10.5 3 21-30 4 20.5 7 31-40 7 30.5 14 41-50 8 40.5 22 51-60 5 50.5 27 61-70 2 60.5 29 71-80 1 70.5 30 ∑ 30

15. Mode is that value of a variety that occurs most often. More precisely, the mode is the value of the variable at which the concentration of the data is maximum. Modal Class : In a frequency distribution, the class having the maximum frequency is called the modal class

16. FORMULA lcb = lower class boundary m-modal class w-width/class size - delta

17. Group the class into three group 1- find the mean group 2- find the median group 3- find the mode

18. Group 1

19. Group 2

20. Group 3