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Understanding the Mean, Mode, and Median in Statistics: A Guide to Central Tendency

This chapter focuses on the concepts of central tendency in statistics, specifically the mean, mode, and median. It explains how to calculate the mean for both ungrouped and grouped data, including direct methods, with practical exercises involving real-world data collection. Examples include determining the average number of plants per house, daily wages of workers, and heartbeats per minute. The chapter aims to enhance understanding of statistical measures and their applications in data analysis.

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Understanding the Mean, Mode, and Median in Statistics: A Guide to Central Tendency

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  1. CHAPTER 14. STASTICS

  2. MEANS OF CENTRAL TENDENCY: MEAN 2.MODE 3.MEDIAN

  3. MEAN OF UNGROUPED DATA If x1, x2, x3, xn are observations with respective frequencies f1, f2, f3, …, fn, then mean is given as X = Mean =

  4. MEAN OF GROUPED DATA Methods to find mean: 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. MEAN OF GROUPED DATA Direct method : X =

  6. MEAN OF GROUPED DATA 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.

  7. EXERCISE 14. 1

  8. EXERCISE 14. 1

  9. EXERCISE 14. 1 Here, 20 162 So, Mean = = = 8.1 ANS. The mean number of plants is 8.1 per house.

  10. EXERCISE 14. 1 2. Consider the following distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using an appropriate method.

  11. EXERCISE 14. 1

  12. EXERCISE 14. 1 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. EXERCISE 14. 1 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.

  15. EXERCISE 14. 1

  16. EXERCISE 14. 1

  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. EXERCISE 14. 1 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. Find the mean number of mangoes kept in a packing box. Which method of finding mean did you choose?

  19. EXERCISE 14. 1

  20. EXERCISE 14. 1

  21. EXERCISE 14. 1

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