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

Transcript

Question 5 Find the median of 8, 10, 19, 23, 26, 34, 40, 41, 41, 48, 51, 55, 70, 84, 91, 92. (i) If we include one value to the data (in the given list) without affecting the median, what could that value be? (ii) If we include two values to the data without affecting the median what could the two values be? (iii) If we remove one value from the data without affecting the median what could the value be?Let’s find Median First Median Writing data in ascending order 8, 10, 19, 23, 26, 34, 40, 41, 41, 48, 51, 55, 70, 84, 91, 92 Number of terms = 16 Since number of observations is even, We use the average of the two middle numbers Now, Median = ((𝑛/2)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 + (𝑛/2 + 1)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 )/2 = ((16/2)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 + (16/2 + 1)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 )/2 = (8^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 + (8 + 1)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 )/2 = (𝟖^𝒕𝒉 𝒐𝒃𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏 + 𝟗^𝒕𝒉 𝒐𝒃𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏 )/𝟐 = (41 + 41)/2 = 41 Now, let’s do our question (i) If we include one value to the data (in the given list) without affecting the median, what could that value be? Since there 16 numbers, if we add one number New number of terms = 17 In that case, 9th term will be Median Our numbers right now are 8, 10, 19, 23, 26, 34, 40, 41, 41, 48, 51, 55, 70, 84, 91, 92 If we need Median = 41, we just need to add any number on the left of 41, i.e. any number less than 41 In such a case, our 8th term will beomce 9th term and our Median will remain same Thus, the value could be 2 (ii) If we include two values to the data without affecting the median what could the two values be? Here, we need to keep our middle two terms as 41. So, we add one number on left of 41, i.e. number less than 41 And, we add one number on right of 41, i.e. number larger than 41 Let’s add numbers 1, and 100 (iii) If we remove one value from the data without affecting the median what could the value be? Since there 16 numbers, if we remove one number New number of terms = 15 In that case, 8th term will be Median Our numbers right now are 8, 10, 19, 23, 26, 34, 40, 41, 41, 48, 51, 55, 70, 84, 91, 92 Since both 8th and 9th term are 41, If we remove any number on the left of 41, our 7th and 8th term will be 41 If we remove any number on the right of 41, our 7th and 8th term will be 41 Thus, let’s remove 92 = 77/2 = 38.5 Thus, Median of onion prices in Wahapur = ₹ 38.5/kg