Question 1 of 15intermediate🔧 ApplyNumerical3 marks
Find the mean of the following data and share your observations: (i) The first 50 natural numbers. (ii) The first 50 odd numbers. (iii) The first 50 multiples of 4.
(i)
Answer
The mean of the first 50 natural numbers is 25.5.
(ii)
Answer
The mean of the first 50 odd numbers is 50.
(iii)
Answer
The mean of the first 50 multiples of 4 is 102.
Explanation
(i) Using the formula for sum of first n natural numbers: n(n+1)/2 = /2 = 1275. Dividing by 50 gives 25.5. (ii) The sum of first n odd numbers equals n². So sum = 50² = 2500. Mean = 2500/50 = 50. (iii) First 50 multiples of 4 form an AP: 4, 8, 12, ..., 200. Sum = 50/2 × (4 + 200) = 5100. Mean = 5100/50 = 102.