2. 1.MEAN 2.MODE 3.MEDIAN

3. If x 1, x 2, x 3, x n are observations with respective frequencies f 1, f 2, f 3, …, f n, then mean is given as X = Mean =

4. Methods to find mean: 1.Direct method : Class mark = For a class interval 10 – 20, class mark is 15. For a class interval 15- 35, class interval is 25.

5. 1.Direct method : X =

6. EXERCISE 14. 1 1. A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house. Number of plants 0-22-44-66-88-1010-1212-14 Number of houses 1215623

7. Class interval Class mark x Frequency f fx 0-21 2-42 4-61 6-85 8-106 10-122 12-143

8. Class interval Class mark x Frequency f fx 0-2111 2-4326 4-6515 6-87535 8-109654 10-1211222 12-1413339 TOTAL20

9. Here, 20 162 So, Mean = = ANS. The mean number of plants is 8.1 per house. = 8.1

10. 2. Consider the following distribution of daily wages of 50 workers of a factory. Daily wages ( in Rs) 100-120120-140140-160160-180180-200 Number of workers 12148610 Find the mean daily wages of the workers of the factory by using an appropriate method.

11. Class interval Class mark x Frequency f fx 100-12012 120-14014 140-1608 160-1806 180-20010 TOTAL50

12. Class interval Class mark x Frequency f di = x- 150fi x di 100-12011012-40-480 120-14013014-20-280 140-160150800 160-180170620120 180-2001901040400 TOTAL = 50 = ? Let assumed mean A = 150 Let assumed mean A = 150

13. So, mean = A + ( assumed mean method) = 150 + ( ) = 150- 4.8 = 145.2 So, the mean daily wage of the workers = Rs. 145.20

14. 4. Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarised as follows. Find the mean heart beats per minute for these women choosing a suitable method. Number of heart beats per minute 65- 68 68-7171-7474-7777-8080-8383-86 Number of women 2438742

15. Class interval Class mark x Frequency f di = x- 75.5fi x di 65-6866.52 68-7169.54 71-7472.53 74-7775.58 77-8078.57 80-8381.54 83-8684.52 TOTAL =30 = ?

16. Class interval Class mark x Frequency f d = x- 75.5f x d 65-6866.52-9-18 68-7169.54-6-24 71-7472.53-3-9 74-7775.5800 77-8078.57321 80-8381.54624 83-8684.52918 TOTAL =30 = ?

17. So, mean = A + ( assumed mean method) = 75.5 + ( ) = 75.5 + 0.4 = 75.9 Ans. The mean heart beats per minute = 75.9

18. 5. In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes. Number of mangoes 50-5253-5556-5859-6162-64 Number of boxes 1511013511525 Find the mean number of mangoes kept in a packing box. Which method of finding mean did you choose?

19. Class interval New CI. Class mark x Frequenc y f di = x- 75.5 fi x di 65-6866.52-9-18 68-7169.54-6-24 71-7472.53-3-9 74-7775.5800 77-8078.57321 80-8381.54624 83-8684.52918 TOTAL =30 = ?