Question 3 - Figure it out - Page 129-134 - Chapter 5 Class 7 - Connecting the Dots... (Ganita Prakash II)

Transcript

Question 3 The marks (out of 100) obtained by a group of students in a General Knowledge quiz are 85, 76, 90, 85, 39, 48, 56, 95, 81 and 75. Another group’s scores in the same quiz are 68, 59, 73, 86, 47, 79, 90, 93 and 86. Compare and describe both the groups performance using, mean and median.Let’s find the Mean and Median for both data For Group 1 Finding Median Writing data in ascending order 39, 48, 56, 75, 76, 81, 85, 85, 90, 95 Number of observations = 10 Since number of observations is even, Median is the average of the two middle numbers Now, Median = (5^𝑡ℎ 𝑡𝑒𝑟𝑚 + 6^𝑡ℎ 𝑡𝑒𝑟𝑚)/2 = (76 + 81)/2 = 157/2 = 78.5 Thus, Median score for Group 1 = 78.5 Finding Mean Now, Mean = (𝑆𝑢𝑚 𝑜𝑓 𝑠𝑐𝑜𝑟𝑒𝑠 )/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠) = (39 + 48 + 56 + 75 + 76 + 81 + 85 + 85 + 90 + 95)/10 = 730/10 = 73 Thus, Mean score for Group 1 = 73 For Group 2 Finding Median Writing data in ascending order 47, 59, 68, 73, 79, 86, 86, 90, 93 Number of observations = 9 Since number of observations is odd, Median is the middle number Now, Median = 5th term = 79 Thus, Median score for Group 2 = 79 Finding Mean Now, Mean = (𝑆𝑢𝑚 𝑜𝑓 𝑠𝑐𝑜𝑟𝑒𝑠 )/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠) = (47 + 59 + 68 + 73 + 79 + 86 + 86 + 90 + 93)/9 = 681/9 = 75.6 Thus, Mean score for Group 2 = 75.6 Comparison Group 2 performed slightly better because both their mean (75.6 vs 73) and median (79 vs 78.5) are higher than Group 1.