Lesson-14.1-Mean-Median-and-Mode-of-Ungrouped-Data (1).pptx

Central Tendency

1. Lesson 14.1 Mean, Median, and Mode of Ungrouped Data

2. At the end of the lesson, the learners should be able to do the following: I llustrate the measures of central tendency (mean, median, and mode) of statistical data ( M7SP-IVf-1) . C alculate the measures of the central tendency of ungrouped and grouped data ( M7SP-IVf-g-1 ) .

3. Accurately define and illustrate the measures of central tendency (mean, median, and mode) of ungrouped data. Accurately differentiate mean, median, and mode from each other.

4. Appropriately use mean, median, and mode in solving word problems.

5. Let us say that your class took an exam in your math class. You want to summarize the scores that you and your classmates had as a single score. What score should represent everyone’s score?

6. Is it the middle score of the entire class? Is it the most common score in the class? How about if you add everyone’s score and divide the score based on your number?

7. There are various ways on how to summarize the scores of a group of data. These measures are called the measures of central tendency. In this lesson, you will learn about the three measures of central tendency—mean, median, and mode.

8. What is the difference between mean, median, and mode? What are some real-life scenarios where mean, median, or mode are used? How do we choose which measure of central tendency should we use when it is not explicitly stated in a word problem?

9. These are data given as individual values Example: The data set 1, 3, 10, 5, 2, 9 is an example of ungrouped data. Ungrouped Data

10. This is the average value of a set of data. The mean is the sum of all the values in the set of data divided by the number of values. The mean of a sample (or the sample mean ) is denoted by (x bar), and the mean of a population (or the population mean ) is denoted by (mu).   Mean

11. Below is the formula for the sample mean.   Mean summation

12. Example: Find the mean of the ungrouped data: 1, 3, 10, 5, 2, 9.   Mean

13. Example: Thus, the mean of the ungrouped data is 5. Mean

14. This is the middle value of a set of data when arranged in order. To find the median of even number of values, get the mean or average of the two middle values. Median

15. Example: Find the median of the ungrouped data: 1, 3, 10, 5, 2, 9. Arrange the values in increasing or decreasing order.     Median

16. Example: The two middle values are 3 and 5. To get their average, we divide the sum of the numbers by two.   Median

17. Example: Thus, the median of the ungrouped data is .   Median

18. This is the most frequent or common value in a set of data. To get the mode of the data set, we simply find the value that appears most often. There could be more than one mode or no mode at all in a given set of data. Mode

19. Example: In the ungrouped data 1, 3, 10, 5, 2, 9, there is no mode because all values appeared only once. Mode

20. Example 1 : Given the following data, find the median. 36 1 16 4 45 35 13

21. Solution: First, arrange the values in either increasing or decreasing order. 36 1 16 4 45 35 13 1 4 13 16 35 36 45 Example 1 : Given the following data, find the median.

22. Solution: Since the data has an odd number of values, the median is the middle value which is 16 . 36 1 16 4 45 35 13 Example 1 : Given the following data, find the median.

23. Example 2 : What is the mode of the set of values below? 59 57 74 61 61 57 64 61

24. Solution: The mode is the value that occurs the most frequent in a set of data. Observe that the value 61 appears three times while the rest of the values appear only either once or twice. Hence, the mode is .   Example 2 : What is the mode of the set of values below? 59 57 74 61 61 57 64 61

25. Individual Practice: What is the mean of the set of values below? 11 19 27 25 2 12 29

26. Individual Practice: The mean of the following set of data is 65. Find the value of x. 55 74 61 72 61 71 62 x

27. Group Practice : To be done in groups with four members. Suppose you want to get a final grade of 94 in your math class. The final grade is equal to the mean of 6 quizzes you have taken during the semester. Knowing that you scored 90, 89, 97, 96, and 95 in the first five quizzes, what is the minimum score you should get for the 6th quiz? What happens when you scored higher or lower than that?

28. Ungrouped data is a set of data given as individual values. The m ean is the average value of a set of data. This is the sum of all the values in the set of data divided by the number of values. The mean of a sample (or the sample mean) is denoted by ( x bar), and the mean of a population (or the population mean) is denoted by (mu).  

29. The formula for the sample mean is: The median is the middle value of a set of data when arranged in order. To find the median of even number of values, get the mean or average of the two middle values.  

30. The mode is the most frequent or common value in a set of data. To get the mode of the data set, we simply find the value that appears most often. There could be more than one mode or no mode at all in a given set of data.

31. Khan, Salman. “Mean, median, & mode example.” Khan Academy. Retrieved 12 September 2019 from https://bit.ly/2lDPAdU   “Measures of Central Tendency.” Laerd Statistics. Retrieved 12 September 2019 from https://bit.ly/1zX41bK