1. CONFIDENTIAL 1 Median, Mode and Range

2. 2 What you know 1.Find the quotient of: i) 330 ÷ 12 = 27.5 ii) 255.5 ÷ 6= 42.58333…. iii) 237.4 ÷ 4 = 59.35 2. Write the following numbers in ascending order. 23, 45, 28, 56, 32, 62, 36. Ans: 23, 28, 32, 36, 45, 56, 62

3. CONFIDENTIAL 3 Median

4. 4 MEDIAN The median is the middle number in a set of ordered data. When there are even number of data items, you can find the median by adding the two middle numbers and dividing by 2.

5. CONFIDENTIAL 5 Example-1 Find the median of the following data: 4, 9, 0, 7,6, 5, 3. i) Arrange in ascending or descending order: 0, 3, 4, 5, 6, 6, 9. median

6. CONFIDENTIAL 6 Example - 2 Find the median of the following data: (i) 18, 37, 24, 59, 41, 26, 63, 45, 57, 29. Arrange in ascending order, we have 18, 24, 26, 29, 37, 41, 45, 57, 59, 63. There are 10 observations. The middle numbers are 5 th observation and 6 th observation. median = (5 th observation + 6 th observation) 2 = (37 + 41 ) = 39. 2

7. CONFIDENTIAL 7 Now your turn! Find the median of the following data: 4, 9, 7, 5, 12, 3, 8, 10, 11 Ascending order: 3, 4, 5, 7, 8, 9,10, 11, 12 Median= 8

8. CONFIDENTIAL 8 Practice Problems  Find the median of the following data: i. 3, 12, 6, 9, 7, 8, 10, 11, 5, 4, 15. Median= 9 ii. 4, 10, 8, 5, 12, 18, 13, 7, 17, 14. median = 11 iii. 72, 55, 48, 61, 63, 67,73. median =63 iv. 7, 15, 9, 12, 10, 13. Median = 11 v. 365, 225, 118, 132, 240, 350. Median =232.5 vi. 6, 7, 3, 8, 11, 4, 2. Median = 6

9. CONFIDENTIAL 9 Break Let’s have some rest

10. CONFIDENTIAL 10 MODE

11. CONFIDENTIAL 11 Mode The MODE is the data item (s) that appears most often. If all data items occur the same number of times, there is no mode. The mode is especially useful when the data are not numerical.

12. CONFIDENTIAL 12 Example - 1 The list shows the favorite lunches of 15 students. What is the mode. hamburger, pizza, sandwich, pizza, hotdog, sandwich, hotdog, hamburger, hamburger, pizza, sandwich, pizza, pizza, hotdog, sandwich. Pizza occurs more often. So, it is the mode.

13. CONFIDENTIAL 13 Example – 2 Find the mode of the following fruits: orange, apple, mango, pineapple, apple, mango, orange, apple, apple, mango, orange, pineapple. Apple occurs most often. Therefore, apple is the mode.

14. CONFIDENTIAL 14 Do it by yourself Find the mode of the following data: violet, red, violet, orange, orange, violet, red violet, orange, violet, red, orange Violet comes most often. So it is the mode.

15. CONFIDENTIAL 15 Practice problems 1. Find the mode of the following data: 3, 4, 6, 5, 3, 6, 3, 4, 7, 3. Mode = 3 2. The demand of different shirt sizes is given below: size frequency 3637383940 41424344 481210206782 Find the mode. Mode = shirt size of 40, since maximum frequency of size 40 = 20

16. CONFIDENTIAL 16 Practice Problems 3. Find the mode of the following data:  6,10, 8, 10, 6, 8, 7, 8, 4, 8. mode=8  3, 7, 8, 5, 6, 9, 6, 4, 6. mode = 6  25, 31, 27, 29, 32, 25, 28, 25. mode = 25  3, 5, 1, 5, 7, 3, 2, 3. mode = 3  2, 3, 4, 4, 1, 6, 4, 3. mode = 4 4. The demand of shoes of different sizes is as below: Size45678910 Frequ ency 5101215431 Mode is of size 7

17. CONFIDENTIAL 17 More problems 5. ColorBlackgoldensilverwhiteRed Number of Cars 57251510 Which color of the car is most favorite among the customers? Mode = silver

18. CONFIDENTIAL 18 Solve the puzzle http://www.thekidzpage.com/onlinejigsawpuzzles/jigs aw-puzzles/12-piece-jigsaw/03-28-06-sxc- hornet.html

19. CONFIDENTIAL 19 RANGE

20. CONFIDENTIAL 20 Range The range of a data set is the difference between the least and the greatest values.

21. CONFIDENTIAL 21 Example - 1 Find the range for each data set: 36, 21, 9, 34, 10, 4, 35, 5, 30, 29,32. Method: Subtract the least from the greatest value. Greatest value = 36; least value = 4 Range = 36 – 4 = 32.

22. CONFIDENTIAL 22 Example - 2 The prize of tickets for a theatre show are $46, $ 35, $ 32, $40,$ 20,$45, $33, $ 36 Range = $46 - $ 20 = $ 26.

23. CONFIDENTIAL 23 Your turn Find the range of the following data: 7, 2, 6, 1, 7, 6, 9, 1, 8, 4, 2, 3, 10. Range = 10 – 1 = 9

24. CONFIDENTIAL 24 More problems Find the range of the following data: i. 3000, 5000, 10,000, 12,000, 9000, 13000. Range = 13000 – 3000 = 10000 ii. 20,30,42,25,15,5,4. Range = 42 – 4 =38 iii. 2300, 2700, 3600, 4100, 5400, 6000. Range = 6000 – 2300 = 3700 iv. 10, 5, 6, 3, 8, 7, 4. Range = 10 – 3 = 7 v. 40, 25, 20, 35, 15, 28, 10, 45, 36, 32, 35, 15, 30, 12. Range = 40 – 10 = 30

25. CONFIDENTIAL 25 That’s all for today