Question 10 - Figure it out - Page 129-134 - Chapter 5 Class 7 - Connecting the Dots... (Ganita Prakash II)

Transcript

Question 10 (a) Aditi likes solving puzzles. She recently started attempting the ‘Easy’ level Sudoku puzzles. The time she took (in seconds) to solve these puzzles are — 410, 400, 370, 340, 360, 400, 320, 330, 310, 320, 290, 380, 280, 270, 230, 220, 240. The first nine values correspond to Week 1 and the rest to Week 2. (a) Construct a dot plot below showing the data for both weeks.Now, our data is Week 1: 410, 400, 370, 340, 360, 400, 320, 330, 310 Week 2: 320, 290, 380, 280, 270, 230, 220, 240 Putting in a dot plot Question 10 (b) Aditi likes solving puzzles. She recently started attempting the ‘Easy’ level Sudoku puzzles. The time she took (in seconds) to solve these puzzles are — 410, 400, 370, 340, 360, 400, 320, 330, 310, 320, 290, 380, 280, 270, 230, 220, 240. The first nine values correspond to Week 1 and the rest to Week 2. (b) Describe the mean, median, and any observations you may have about the data.For Week 1 Finding Median Writing data in ascending order 310, 320, 330, 340, 360, 370, 400, 400, 410 Number of observations = 9 Since number of observations is odd, Median is the middle number Now, Median = 5th term = 360 Thus, Median for Week 1 = 360 seconds Finding Mean Now, Mean = (𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑆𝑒𝑐𝑜𝑛𝑑𝑠)/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑡𝑒𝑚𝑝𝑡𝑠) = (310+320+330+340+360+370+400+400+410)/9 = 3240/9 = 360 seconds Thus, Mean for Week 1 = 360 seconds For Week 2 Finding Median Writing data in ascending order 220, 230, 240, 270, 280, 290, 320, 380 Number of observations = 8 Since number of observations is even, Median is the average of two middle numbers Now, Median = (4^𝑡ℎ 𝑡𝑒𝑟𝑚 + 5^𝑡ℎ 𝑡𝑒𝑟𝑚)/2 = (270 + 280)/2 = 275 Thus, Median for Week 2 = 275 seconds Finding Mean Now, Mean = (𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑆𝑒𝑐𝑜𝑛𝑑𝑠)/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑡𝑒𝑚𝑝𝑡𝑠) = (220+230+240+270+280+290+320+380)/8 = 2230/8 = 278.75 seconds Thus, Mean for Week 2 = 278.75 seconds Observations Aditi improved significantly in Week 2! Her average time dropped from 360 seconds to roughly 279 seconds. She is solving puzzles much faster.