Question 1 - Figure it out - Page 112, 113 - Chapter 5 Class 7 - Connecting the Dots... (Ganita Prakash II)

Transcript

Question 1 Find the median of onion prices in Yahapur and Wahapur.The data is Month Yahapur January 25 February 24 March 26 April 28 May 30 June 35 July 39 August 43 September 49 October 56 November 59 December 44 Month Wahapur January 19 February 17 March 23 April 30 May 38 June 35 July 42 August 39 September 53 October 60 November 52 December 42For Yahapur Writing data in ascending order 24, 25, 26, 28, 30, 35, 39, 43, 44, 49, 56, 59 Number of months = 12 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 = ((12/2)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 + (12/2 + 1)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 )/2 = (6^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 + (6 + 1)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 )/2 = (𝟔^𝒕𝒉 𝒐𝒃𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏 + 𝟕^𝒕𝒉 𝒐𝒃𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏 )/𝟐 = (35 + 39)/2 = 74/2 = 37 Thus, Median of onion prices in Yahapur = ₹ 37/kg For Wahapur Writing data in ascending order 17, 19, 23, 30, 35, 38, 39, 42, 42, 52, 53, 60 Number of months = 12 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 = ((12/2)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 + (12/2 + 1)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 )/2 = (6^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 + (6 + 1)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 )/2 = (𝟔^𝒕𝒉 𝒐𝒃𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏 + 𝟕^𝒕𝒉 𝒐𝒃𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏 )/𝟐 = (38 + 39)/2 = 77/2 = 38.5 Thus, Median of onion prices in Wahapur = ₹ 38.5/kg