Question 11 - Figure it out - Page 113-116 - Chapter 5 Class 8 - Tales by Dots and Lines (Ganita Prakash II)

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Question 11 A dart-throwing competition was organised in a school. The number of throws participants took to hit the bull’s eye (the centre circle) is given in the table below. Describe the data using its minimum, maximum, mean and median.Here, Total number of students = 1 + 0 + 0 + 1 + 4 + 9 + 12 + 15 + 10 + 10 = 62 And, Number of trials = 1 × 1 + 2 × 0 + 3 × 0 + 4 × 1 + 5 × 4 + 6 × 9 + 7 × 12 + 8 × 15 + 9 × 10 + 10 × 10 = 473 = 473 Now, Minimum: The lowest number of throws to hit the bullseye was 1. Maximum: The highest number of throws was 10. Finding Mean Mean = (𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠) = 473/62 = 7.62 (approx.) Finding Median Since Total number of students = 62 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 = ((62/2)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 + (62/2 + 1)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 )/2 = (31^𝑠𝑡 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 + (31 + 1)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 )/2 = (𝟑𝟏^𝒔𝒕 𝒐𝒃𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏 +𝟑𝟐^𝒏𝒅 𝒐𝒃𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏 )/𝟐 Thus, median is the average of the 31st and 32nd values. Counting the dots from left to right, both the 21st and 22nd dots fall in the "4" column. The median is 4. Thus, median is the average of the 31st and 32nd values. If we keep a running total of the frequencies from left to right, the 31st and 32nd values both fall inside the column for 8 throws. Thus, median is 8.