Question 3 - Figure it out - Page 112, 113 - Chapter 5 Class 7 - Connecting the Dots... (Ganita Prakash II)

Transcript

Question 3 Rintu takes care of a date-palm tree farm in Habra. The heights of the trees (in feet) in his farm are given as: 50, 45, 43, 52, 61, 63, 46, 55, 60, 55, 59, 56, 56, 49, 54, 65, 66, 51, 44, 58, 60, 54, 52, 57, 61, 62, 60, 60, 67. Fill the dot plot, and mark the mean and median. How would you describe the heights of these palm trees? Can you think of quicker ways to find the mean? How many trees are shorter than the average height?Let’s first find Median & Mean Here, Number of trees = 30 Finding Median Writing data in ascending order 43, 44, 45, 46, 49, 50, 51, 52, 52, 54, 54, 55, 55, 56, 56, 56, 57, 58, 59, 60, 60, 60, 60, 61, 61, 62, 63, 65, 66, 67 Since number of observations is even, We use the average of the two middle numbers Now, Median = ((30/2)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 + (30/2 + 1)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 )/2 = ((30/2)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 + (30/2 + 1)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 )/2 = (15^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 + (15 + 1)^𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 )/2 = (〖𝟏𝟓〗^𝒕𝒉 𝒐𝒃𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏 + 〖𝟏𝟔〗^𝒕𝒉 𝒐𝒃𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏 )/𝟐 = (56 +56)/2 = 56 Thus, Median Height = 56 feet Finding Mean Now, Mean = (𝑆𝑢𝑚 𝑜𝑓 ℎ𝑒𝑖𝑔ℎ𝑡𝑠)/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑒𝑒𝑠) = (43+ 44+ 45+ 46+ 49+ 50+ 51+ 52+ 52+ 54+54+ 55+55+ 56+ 56+ 56+ 57+ 58+ 59+ 60+ 60+ 60+ 60+ 61+ 61+ 62,+63+ 65+ 66+ 67)/30 = 1667/30 = 55.56… Thus, Mean Height = 55.56… feet Putting in a dot plot Now, we need to answer some questions Quicker way to find the Mean? Instead of adding huge numbers, you can guess an average (like 55). Then see how much each number is above or below 55, add those small differences up, and adjust your guess. This is called the "Assumed Mean Method." How many trees are shorter than average? The average is 𝟓𝟓.𝟓𝟕. Looking at our sorted list, count how many numbers are less than 55.57 . (Numbers: 43,…,55,55 ) Thus, there are 13 trees shorter than the average height.