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

Transcript

Question 5 Consider a group of 17 students with the following heights (in cm): 106, 110, 123, 125, 117, 120, 112, 115, 110, 120, 115, 102, 115, 115, 109, 115, 101. The sports teacher wants to divide the class into two groups so that each group has an equal number of students: one group has students with height less than a particular height and the other group has students with heights greater than the particular height. Suggest a way to do this. Can you guess the age of these students based on the tabular data in the ‘Telling Tall Tales’ section?In statistics, whenever you want to cut a population in half (50% vs 50%), you always use the Median. If you want to find the "average height," you use the Mean. There are 17 students. To divide them equally (or as close as possible), we need to find the middle height (the median). Writing data in ascending order 101, 102, 106, 109, 110, 110, 112, 115, 115, 115, 115, 115, 117, 120, 120, 123, 125. Since number of observations is odd, Median is the middle number Now, Median = 9th term = 115 cm Diving into groups The teacher can divide the groups into "Students 115 cm and taller" and "Students shorter than 115 cm". Or, since there are many students exactly at 115, they could make the split at 114 cm. Thus, our groups become Group A (Shorter than 114cm): 101, 102, 106, 109, 110, 110, 112 (7 students). Group B (115cm and taller): 115 (5 students), 117, 120, 120, 123, 125 (10 students). Note: Since there are so many students at 115cm, it is hard to get perfectly equal groups without splitting the 115s Diving into groups The teacher can divide the groups into "Students 115 cm and taller" and "Students shorter than 115 cm". Or, since there are many students exactly at 115, they could make the split at 114 cm. Thus, our groups become Group A (Shorter than 114cm): 101, 102, 106, 109, 110, 110, 112 (7 students). Group B (115cm and taller): 115 (5 students), 117, 120, 120, 123, 125 (10 students). Note: Since there are so many students at 115cm, it is hard to get perfectly equal groups without splitting the 115s Guessing age of these students We use this table Age 1989 1999 2009 2019 5 101.3 100 102.4 101.7 105.1 104 107.1 107.2 6 107.5 106 108.7 107.5 111 109.7 113.1 112.9 7 113 111.4 114.2 112.6 116.2 114.8 118.6 118 8 118.1 116.5 119.2 117.5 120.9 119.6 123.5 122.7 9 122.9 121.7 123.9 122.4 125.2 124.5 128.1 127.6 10 127.5 127.3 128.3 127.8 129.4 129.9 132.6 132.8 11 132.2 133.4 132.8 133.6 133.7 135.7 137 138.6 12 137.7 139 138 139.1 138.9 141.1 142.2 143.8 13 144.2 143.2 144.3 143.1 145.2 145.1 148.4 147.7 14 150.6 146.2 150.5 146.1 151.5 148 154.4 150.4 15 155.4 148.5 155.2 148.4 156.3 150.1 159 152.4 16 158.9 150.1 158.7 150.1 159.9 151.6 162.3 153.8 17 161.3 151.2 161.4 151.3 162.6 152.6 164.6 154.7 18 162.9 151.8 163.2 152.1 164.3 153 166 155.2 19 163.5 151.9 164.2 152.4 165.1 153 166.5 155.2 Since height is from 101 to 125 cm They are from Age 5 to 9