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

Transcript

Question 7 The weights of some sumo wrestlers and ballet dancers are: Sumo wrestlers: 295.2 kg, 250.7 kg, 234.1 kg, 221.0 kg, 200.9 kg. Ballet dancers: 40.3 kg, 37.6 kg, 38.8 kg, 45.5 kg, 44.1 kg, 48.2 kg. Approximately how many times heavier is a sumo wrestler compared to a ballet dancer?We have to compare two groups that are extremely different (like Sumos and Dancers), To compare, we find a "Representative Value"— that could be Mean or Median We usually choose Mean unless there is an outlier In both data, there is no outlier (either very high weight or very low weight – in that data) This means there is no very light sumo lesser or very heavy ballerina Thus, since there is no outlier, we choose Mean Weight to compare Finding mean weight for each Approximate Mean Weight for Sumo Data is 295.2 kg, 250.7 kg, 234.1 kg, 221.0 kg, 200.9 kg We use approx values since it is given we need to find approximately how many times heavier a sumo is to ballet dancer So, we use 295 kg, 250 kg, 235 kg, 220 kg, 200 kg Now, Approximate Mean weight = (𝑆𝑢𝑚 𝑜𝑓 𝑤𝑒𝑖𝑔ℎ𝑡 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑠𝑢𝑚𝑜𝑠)/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑢𝑚𝑜𝑠) = (295 + 250 + 235 + 220 + 200)/5 = 𝟏𝟐𝟎𝟎/𝟓 = 240 kg Thus, Approximate Mean weight for sumos = 240 kg Approximate Mean Weight for Ballet Dancers Data is 40.3 kg, 37.6 kg, 38.8 kg, 45.5 kg, 44.1 kg, 48.2 kg We use approx values since it is given we need to find approximately how many times heavier a sumo is to ballet dancer So, we use 40 kg, 38 kg, 39 kg, 46 kg, 44 kg, 48 kg Now, Approximate Mean weight = (𝑆𝑢𝑚 𝑜𝑓 𝑤𝑒𝑖𝑔ℎ𝑡 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑠𝑢𝑚𝑜𝑠)/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑢𝑚𝑜𝑠) = (40 + 38 + 39 + 46 + 44 + 48)/5 = 𝟐𝟓𝟓/𝟔 = 42.5 kg (approx) Thus, Approximate Mean weight for ballet dancer = 42.5 kg Finding how many times heavier is a sumo wrestler compared to a ballet dancer Now, Approximate Mean weight for sumos = 240 kg Approximate Mean weight for ballet dancer = 42.5 kg Thus, Sumo is heavier than ballet dancer by = 𝟐𝟒𝟎/(𝟒𝟐.𝟓) = 240 × 𝟏/(𝟒𝟐.𝟓) = 240 × 𝟏/(𝟒𝟐𝟓/𝟏𝟎) = 240 × 𝟏𝟎/𝟒𝟐𝟓 = 𝟐𝟒𝟎𝟎/𝟒𝟐𝟓 = 5.647… Thus, A sumo wrestler is approximately 5 to 6 times heavier than a ballet dancer.