Question 2 - Figure it out - Page 112, 113 - Chapter 5 Class 7 - Connecting the Dots... (Ganita Prakash II)

Transcript

Question 2 Sanskruti asked her class how many domestic animals and pets each had at home. Some of the students were absent. The data values are 0, 1, 0, 4, 8, 0, 0, 2, 1, 1, 5, 3, 4, 0, 0, —, 10, 25, 2, — , 2, 4. Find the mean and median. How would you describe this data?The dashes (—) represent absent students, so we do not count them. We only calculate using the actual numbers provided. Thus, Number of students = 21 Finding Median Writing data in ascending order 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 8, 10, 25 Since number of observations is odd, Median will be the middle number Thus, Median = ((𝒏 + 𝟏)/𝟐)^𝒕𝒉 observation = ((21 + 1)/2)^𝑡ℎ observation = (𝟐𝟐/𝟐)^𝒕𝒉 observiation = 11th observation = 2 Thus, Median is 2 Finding Mean Now, Mean = (𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑛𝑖𝑚𝑎𝑙𝑠)/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠) = (0+0+0+0+0+0+0+1+1+1+2+2+2+3+4+4+4+5+8+10+25)/21 = 72/21 = 24/7 = 3.43.. Thus, Mean is 3.43.. Description of the Data Most students have very few animals (0, 1, or 2). There is one student with 25 animals! This is called an outlier because it is way bigger than the rest. It pulls the mean (average) up, making it look like students have more pets than they really do. The median (2) represents the class better here.