Question 1 - Figure it out - Page 113-116 - Chapter 5 Class 8 - Tales by Dots and Lines (Ganita Prakash II)

Transcript

Question 1 Find the mean of the following data and share your observations: (i) The first 50 natural numbers.Natural numbers are numbers starting from 1 like 1, 2, 3, 4, 5, …. First 50 natural numbers are 1, 2, 3, 4, 5, …. 49, 50 Since numbers are evenly spaced, we can find by averaging the first and last numbers Mean = (𝑭𝒊𝒓𝒔𝒕 𝒏𝒖𝒎𝒃𝒆𝒓 + 𝑳𝒂𝒔𝒕 𝒏𝒖𝒎𝒃𝒆𝒓)/𝟐 = (1 + 50)/2 = 51/2 = 25.5 Let’s actually find the Mean by putting in all numbers and finding Question 1 Find the mean of the following data and share your observations: (ii) The first 50 odd numbers.Odd numbers are 1, 3, 5, 7, 9, …. Now, 50th odd number = 99 Thus, first 50 odd numbers are 1, 3, 5, 7, 9, …. 97, 99 Since numbers are evenly spaced, we can find by averaging the first and last numbers Mean = (𝑭𝒊𝒓𝒔𝒕 𝒏𝒖𝒎𝒃𝒆𝒓 + 𝑳𝒂𝒔𝒕 𝒏𝒖𝒎𝒃𝒆𝒓)/𝟐 = (1 + 99)/2 = 100/2 = 50 Question 1 Find the mean of the following data and share your observations: (iii) The first 50 multiples of 4.Multiples of 4 are numbers which are in table of 4, i.e. 4, 8, 12, 16, 20, …. Now, 50th multiple of 4 = 50 × 4 = 200 Thus, first 50 multiples of 4 are 4, 8, 12, 16, 20, …. 200 Since numbers are evenly spaced, we can find by averaging the first and last numbers Mean = (𝑭𝒊𝒓𝒔𝒕 𝒏𝒖𝒎𝒃𝒆𝒓 + 𝑳𝒂𝒔𝒕 𝒏𝒖𝒎𝒃𝒆𝒓)/𝟐 = (4 + 200)/2 = 204/2 = 102